# Chapter 7 Energy and Energy Balances

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 CBE14, Levicky Chapter 7 Energy and Energy Balances The concept of energy conservation as expressed by an energy balance equation is central to chemical engineering calculations. Similar to mass balances studied previously, a balance on energy is crucial to solving many problems. System A system is an obect or a collection of obects that an analysis is done on. The system has a definite boundary, called the system boundary, that is chosen and specified at the BEGINNING of the analysis. Once a system is defined, through the choice of a system boundary, everything external to it is called the surroundings. All energy and material that are transferred out of the system enter the surroundings, and vice versa. In the general case there are very few restrictions on what a system is; a system can have a nonzero velocity, a nonzero acceleration, and a system can even change in size with time. An isolated system is a system that does not exchange heat, work, or material with the surroundings. If heat and work are exchanged across a system s boundary, but material is not, it is a closed system. An open system can exchange heat, work, and material with the surroundings. Examples. Discuss each situation below as approximating an isolated, a closed, or an open system. (i) A river. (ii) The interior of a closed can of soda. (iii) The interior of a closed refrigerator that is turned on. (iv) The interior of a closed refrigerator that is turned off. 1

2 CBE14, Levicky State of a System Once a system is defined, a certain number of variables will specify its state fully. For example, one may need to provide the temperature, pressure, composition, total amount of material, velocity, and position in order to specify a system s state. The exact information that is needed to specify the state of a system depends on the type of system and the analysis to be performed. State Functions and State Properties The state of a system can be changed, for example by increasing its temperature or changing its composition. Properties of the system whose change depends only on the initial (before) and final states of the system, but not on the manner used to realize the change from the initial to the final state, are referred to as state properties or state functions. In other words, the change in a state function or state property X, between some final (state ) and initial (state 1) situations, can be expressed as X = X X final initial change in X X state X state1 (1) In equation 1, X final only depends on the final state of the system, and X initial only on the initial state of the system. Equation 1 does not require any information whatsoever as to how the system got from the initial to the final state, since X does not depend on the details of the path followed. Example. Which of the below examples represent changes in state functions? (i) (ii) Work done to climb from the bottom (state 1) to the top (state ) of a mountain. Change in gravitational energy of an obect when it is raised from the bottom (state 1) to the top (state ) of a mountain. (iii) Change in density of water in a pot when it is heated from 0 o C (state 1) to 50 o C (state ). (iv) Amount of heat liberated from burning gas in a stove in order to realize a temperature change of the water in a pot from 0 o C (state 1) to 50 o C (state ). (This requires some thought )

3 CBE14, Levicky Forms of Energy: The First Law of Thermodynamics Energy is often categorized as: A. Kinetic Energy B. Potential Energy C. Internal Energy Kinetic Energy A system s kinetic energy is associated with directed motion (e.g. translation, rotation) of the system. Translation refers to straight line motion. The kinetic energy E k of a moving obect of mass m and travelling with speed u is given by, 1 mu Ek = () Note that u is measured relative to a frame of reference that defines what is stationary. E k has units of energy, m of mass, and u of length/time. How could the kinetic energy of a system change? Is kinetic energy a state function? Potential Energy Potential energy of a system is due to the position of the system in a potential field. There are various forms of potential energy, but only gravitational potential energy will be considered in this course. The gravitational potential energy of an obect of mass m at an elevation z in a gravitational field, relative to its gravitational potential energy at a reference elevation z 0, is given by E p = mg( z z0 ) = mgz mgz0 (3) The quantity g is the gravitational acceleration that defines the strength of the gravitational field. Often, the earth s surface is used as the reference and assigned z 0 = 0, in which case mgz represents the gravitational potential energy of the obect relative to its potential energy if it rested on the earth s surface. E p has units of energy, m of mass, g of length/time, and z of length. 3

4 CBE14, Levicky How could the gravitational potential energy of a system change? Is gravitational potential energy a state function? Internal Energy All the energy associated with a system that does not fall under the above definitions of kinetic or potential energy is internal energy. More specifically, internal energy is the energy due to all molecular, atomic, and subatomic motions and interactions. Usually, the complexity of these various contributions means that no simple analytical expression is available from which internal energy can be readily calculated. The internal energy will be represented by the symbol U. What types of events would bring about a change in a system s internal energy? Is internal energy a state function? Enthalpy The enthalpy H of a system is defined by H = U + PV (4) where P is the pressure and V is volume. Let s think about the PV term. We know that PA, where A is the area subected to a pressure P, is the force acting on that area. If a fluid inside a system is displaced through a distance d by the force PA, then the resultant work W done on the system can be calculated as the product of this force times the displacement. In other words, W = PAd. Now note that Ad = V, the volume swept out by the displacement. Thus, an alternate way to write the displacement work is W = PV. This type of work, where pressure results in the displacement of a fluid, will be referred to as flow work. If an amount of fluid of volume V is inserted into a system against a pressure P, the work required to accomplish this is PV. Enthalpy, therefore, can be viewed as the sum of the internal energy of this fluid volume added to the system plus the flow work performed on the system in order to insert the fluid. Enthalpy has units of energy (e.g. J, cal, BTU). 4

5 CBE14, Levicky What types of events would bring about a change in a system s enthalpy? Is enthalpy a state function? Specific Properties The total internal energy, enthalpy, kinetic energy, and potential energy of a system are extensive properties. An extensive property depends on the total number of molecules present in the system and on the system s total size. Often, it is more convenient to refer to the amount of a property per mass of the system. For example, if the system is a fluid phase, one may want to express the amount of internal energy or enthalpy contained in a unit mass of the fluid. If one refers to an amount of a property per mass, one is speaking about a specific property. Specific properties are intensive. Thus, specific volume is volume per mass, specific internal energy is internal energy per mass, and specific enthalpy is enthalpy per mass. Specific properties will be identified by a ^ symbol above them; thus, Vˆ = specific volume (units: volume/mass; e.g. m 3 /kg, ft 3 /lb m ), Uˆ = specific internal energy (units: energy/mass; e.g. J/kg, BTU/lb m ), Ĥ = Uˆ + PVˆ = specific enthalpy (units: energy/mass; e.g. J/kg, cal/g), etc. Given a mass m of a uniform system with a specific property Xˆ, the corresponding extensive amount of X in the system is found using X = m Xˆ. How would you use this expression to calculate the extensive volume of a system? The extensive enthalpy of a system? Reference States The specific internal energy and specific enthalpy of a material are always defined relative to a reference state. The reference state can be chosen to refer to any set 5

6 CBE14, Levicky of conditions, although often it is chosen to be 0 o C and 1 atm. Then, one speaks of Uˆ or Ĥ of a material relative to the value of Uˆ or Ĥ of that material in the reference state. What is the value of Uˆ or Ĥ for the material in its reference state? Now imagine that a system passes from state 1 to state. In general, Uˆ or Ĥ will change when the state of the system changes, with the difference being Uˆ = Uˆ - Uˆ 1 and Ĥ = Ĥ - Ĥ 1 Does the choice of a reference state affect the value of Uˆ or Ĥ? Note that, in calculations, we will only be interested in how much the internal energy or enthalpy changed. That is, we will only need to calculate Uˆ and Ĥ, but not the absolute values of internal energy or enthalpy. Heat When there is a difference in temperature between two points, heat is transferred (flows) from high temperature to the low temperature. By convention the numerical value of heat transferred is positive when it is transferred into the system, thereby increasing the energy contained in the system. That is, if Q is the heat transferred from the surroundings to the system, then Q > 0 means that net heat is transferred to the system so as to increase the energy of the system. If Q < 0, then net heat is transferred from the system to the surroundings, and the system has lost energy. Note that Q has units of energy (e.g. J, BTU, cal). Is the heat transferred in going from state 1 to state a state function? What does transfer of heat mean, physically? That is, what are the molecular level processes that give rise to heat transfer? Work When a force is applied to a system and causes a displacement, then work has been done on that system. By convention the numerical value of work W is positive 6

7 CBE14, Levicky when net work is performed by the system on the surroundings. Thus, W > 0 means that the system has performed work on the surroundings such that the energy remaining in the system has decreased. If W < 0, then surroundings have performed net work on the system so as to increase the system s energy. Work has units of energy (e.g. J, cal, BTU). Is work a state function? Provide two examples of a system undergoing work interactions with its surroundings. Rates vs Amounts Chemical processes use process streams to transport material from one point to another. Consider a stream with a mass flowrate m& (note that we could equivalently have used molar units). The material in the stream carries its kinetic, potential, and internal energy with it. Therefore, the mass transport is perforce accompanied by energy transport. The rates of energy transport (units: energy/time, e.g. J/s, BTU/h) that accompany the material flow in a process stream can be calculated as follows: 1 u m Ek & = & E p m& gz & = U m& U ˆ & = (5) Heat transport and work can be also expressed as rates, with symbols Q & and W &, respectively. The units of Q & and W & are energy/time. Note that units of energy/time are equivalently called units of power. Example Water flows into a process unit through a cm diameter pipe at a volumetric flowrate of.00 m 3 /h. (i) Calculate the rate E & k at which the water stream brings kinetic energy into the unit, in J/s. (ii) What is the reference state used for kinetic energy? (iii) If the pipe is at an elevation z = 100 m (relative to the reference elevation z 0 ), what is the rate at which the stream brings potential energy into the process unit, in J/s? 7

8 CBE14, Levicky 8

9 CBE14, Levicky The General Energy Balance Black Box Analysis: This method of analysis, in the context of process modeling, does not concern itself with how individual process units work. The input and output streams are instead analyzed by applying constraints imposed by nature, namely conservation of mass and conservation of energy. The inner workings of the physical apparatus are not relevant. This course treats process units as black boxes. Future courses will go into detail of how different process units work. The First Law of Thermodynamics is a statement of energy conservation. Although energy cannot be created or destroyed, it can be converted from one form to another (for example, internal energy stored in molecular bonds can be converted into kinetic energy; potential energy can be converted to kinetic or to internal energy, etc.). Energy can also be transferred from one point to another, or from one body to a second body. Energy transfer can occur by flow of heat, by transport of mass (transport of mass is otherwise known as convection), or by performance of work. We ll see examples of these modes of energy transport below. The general energy balance for a process can be expressed in words as: Accumulation of Energy in System = Input of Energy into System Output of Energy from System (6) Now the total energy of a system, as considered above, is composed of kinetic, potential, and internal energies. These energies can be transferred into or out of the system by flow of mass through process streams that bring the various forms of energy with them. In addition, they can be transferred by performance of work, or by flow of heat. Equation 6, after expressing all terms as rates, thus becomes: Rate of Energy Accumulation in System = input streams u u m& Uˆ + + gz m& Uˆ + + gz + Q& W& (7) output streams In the first term on the right of equation 7, runs over all incoming streams, and in the second it runs over all outgoing streams. Note that all terms in equation 7 have units of energy/time. Also, recall the conventions with regard to the sign of the heat and work terms. 9

10 CBE14, Levicky What is the physical meaning of each of the terms in equation 7? Equation 7 can be rewritten in various ways. Let us consider a stationary system (i.e. the system is not experiencing an overall movement in the frame of reference, although its boundary may be deformable). Such a system will in general experience two types of contact work interactions with the surroundings. The first type of work is called shaft work (symbol: W s ) and arises when a part of the boundary of the system is displaced. Shaft work takes place at moving parts of a system s boundary across which there is no mass transport. The force is often exerted by some form of machinery. For example, the surface of a rotating impeller exerts force on the fluid (the fluid being the system) as it stirs the fluid, and hence performs shaft work on the system. Another example is that of a moving wall, such as a piston. The moving piston exerts force and thus performs shaft work on the contained fluid (the fluid again being the system). A second classification of work that we will encounter is flow work. Flow work occurs at areas of a system s boundary across which there is material flowing. The flow work is associated with the force and displacement required to push the material into the system (input streams), or with the force and displacement required to push material out of the system (output streams). A fluid cannot flow unless it creates space for itself when it enters or exits a system. The forces that do the necessary pushing are exerted by particles of the flowing material inside the system on the particles of the material outside the system, and are evaluated at the stream inlets and outlets where the transfer of material into/out of the system takes place. These forces, expressed per area, are the pressure P in the stream. The flow work W fl,, performed by the system on stream in order to transfer a volume of material V into or out of the system, is straightforwardly calculated from the pressure P in the stream W fl, = P V (8) 10

11 CBE14, Levicky Equation 8 assumed that the pressure P is constant for all points at the stream inlet or outlet. Equation 8 can be expressed as a rate of flow work, using the volumetric flowrate V &, W & & fl, = PV (9) W & is the rate at which flow work is performed by the system on stream (the fl, minus sign reflects the convention of positive work when the system performs work on the surroundings). Writing the total rate of work W & = W& s + W& fl, and using equation 9 for the flow work associated with each incoming and outgoing stream, equation 7 can be rewritten as rate of energy accumulation in system = input streams u u m& Uˆ + PVˆ + + gz m& Uˆ + PVˆ + + gz + Q& W& s (10) output streams Equation 10 made use of the fact V& = m& Vˆ. Inserting the definition of specific enthalpy for stream, 10 becomes, Ĥ = Uˆ + P Vˆ, equation rate of energy accumulation in system = input streams u u m & Hˆ + + gz m& Hˆ + + gz + Q& W& s (11) output streams The rate of accumulation term can be broken down into rates of accumulation of kinetic, potential, and internal energies: de dt k dep du u u + + = m & Hˆ + + gz m& Hˆ + + gz + Q& W& s dt dt input streams output streams (1) where E k, E P, and U are the total kinetic, potential, and internal energies of the system. Note that the time derivative de k /dt is the rate of change of the total kinetic energy of the system with time; by definition, this is the rate of accumulation of the 11

12 CBE14, Levicky total kinetic energy. Analogous comments apply to the other two accumulation terms, de P /dt and du/dt. Integration of equation 1 with respect to time, from an initial to a later (final) time yields, (E kf E ki ) + (E Pf E Pi ) + (U f U i ) = input streams m Hˆ u + + gz output streams m Hˆ u + + gz + Q W s or, E k + E P + U = input streams m Hˆ u + + gz output streams m Hˆ u + + gz + Q W s (13) where E k = (E kf E ki ), E P = (E Pf E Pi ), and U = (U f U i ). m is the amount of mass transferred into the system by stream in the period between the initial and final times. The specific enthalpy Ĥ, mass flowrate m&, flowrate velocity u, and elevation z of each stream are assumed to have remained constant during the period from the initial to the final time. Finally, Q is the total amount of heat added to the system, and W s is the total shaft work performed by the system on the surroundings, between the initial and final times. Equations 10 through 13 serve as different forms of the general energy balance for this course. Examples. How does equation 13 simplify for an isolated system? What does equation 13 look like if applied to a closed system at steady state? How does equation 1 simplify for a closed system at steady state? 1

13 CBE14, Levicky How does equation 1 simplify for an open system at steady state? Comments. For systems with no significant heat exchange with surroundings Q = 0. Such a system is said to be adiabatic. The absence of any heat transfer can be due to perfect thermal insulation or the fact that the system and surroundings are at the same temperature. If the system is not accelerating, then E k = 0. If the system is not experiencing a displacement in the direction of the gravitational field, then E P = 0. If there is no motion along the system boundary, then W s = 0. But note that a nonzero W s is possible even if there is no motion perpendicular to the system s boundary, since the motion performing the shaft work could still be tangential to the boundary. Steam Tables The steam tables are a tabulation of the thermodynamic parameters for water in liquid and vapor phases. Information is provided for saturated liquid, saturated steam (i.e. saturated water vapor), and for superheated steam (i.e. superheated water vapor). Saturated liquid and saturated steam can coexist in a vapor liquid equilibrium. Superheated steam would have to be cooled to its dew point to become saturated. The steam tables provide the following parameters: (i) vapor pressure of saturated water as a function of temperature (equivalently, the boiling point of liquid water as a function of pressure) (ii) the specific volume Vˆ of liquid water and of steam (iii) the specific internal energies of liquid water and of steam relative to a reference state of liquid water at the triple point (iv) the specific enthalpy of liquid water and of steam relative to a reference state of liquid water at the triple point (v) the heat of vaporization of water, given by the difference between the enthalpies of the saturated steam and of the saturated liquid There are three steam tables in appendices B.5 through B.7. Tables B.5 and B.6 provide data for saturated steam and saturated liquid. These tables apply to vaporliquid coexistence. All of the above intensive properties are presented for both the 13

14 CBE14, Levicky liquid and the vapor phases. Appendix B.7 gives, in addition, the properties for superheated steam. For any of the tables you may need to use linear interpolation between the tabulated conditions to estimate the property of interest. Solving Material and Energy Balance Problems The following steps are helpful in solving problems that combine material and energy balance calculations. 1). Since material balances have to be obeyed even if an energy balance is to be performed, the first thing to do is to solve the material balance part of the problem (i.e. choose a basis, make a flowchart, identify your unknows, perform a degrees of freedom analysis, write equations, solve). ). If an energy balance calculation is required in addition, there will be an extra unknown in the problem. This unknown may be a temperature, amount of heat added, or some other variable that appears in the energy balance. The extra equation you ll use to solve for this additional variable is the energy balance. To begin, identify the system and write the appropriate form of the energy balance for it (i.e. closed, open, isolated). Also, delete any terms from the energy balance that are either zero or negligible compared to the other terms. For example, if steady state applies then the de dt de dt du + dt k P + terms can be set to zero. If no shaft work is taking place, then W s = 0. Other simplifications may apply based on the given information. 3). For each species that you need Ĥ or Uˆ for, you will need to choose a reference state. If using data from an external source (i.e. tables, graphs) the reference state will be specified in that source. If you will be calculating the internal energies or enthalpies yourself (methods for doing this will be discussed in Chapters 8 and 9), then you will need to decide what reference state to use. Often, it is convenient to choose one of the inlet or outlet conditions as the reference state, as then the Ĥ or Uˆ for that stream become zero, thus simplifying the calculations. 4). Make a list of all the terms in the energy balance that you will need to calculate or look up in order to solve for the unknown of interest. This list may include internal energies, enthalpies, elevations, mass flowrates (mass flowrates were presumably already calculated in step 1), etc. 14

15 CBE14, Levicky 5). Calculate all the quantities identified in step 4. 6). Solve the energy balance for the remaining unknown of interest. To do so, you will need to insert the values of all the other terms appearing in the energy balance, as identified and calculated in steps 4 and 5. Example A gas is contained in a cylinder fitted with a movable piston. The initial temperature of the gas is 5 o C. The cylinder is next placed in boiling water, and.00 kcal of heat is transferred to the gas, raising its temperature to 100 o C. During this step, the piston is not allowed to move. What happens to the pressure of the gas? In a second step, the piston is released and the gas does 100 J of work in moving the piston to its new equilibrium position. The final gas temperature is 100 o C (note that the cylinder is still immersed in the boiling water). Write the energy balance equation for each of the two steps. In each case, solve for the unknown term in the equation. The gas is assumed to be ideal, and effects due to gravitational potential energy are negligible. 15

16 CBE14, Levicky 16

17 CBE14, Levicky Example The specific internal energy of helium at 300 K and 1 atm is 3800 J/mol, and the specific molar volume at the same temperature and pressure is 4.63 L/mol. Calculate the specific enthalpy of helium at this temperature and pressure, and the rate at which enthalpy is transported by a stream of helium at 300 K and 1 atm with a molar flow rate of 50 kmol/h. 17

18 CBE14, Levicky Example Five hundred kg/h of steam drives a turbine. The steam enters the turbine at 44 atm and 450 o C at a linear velocity of 60 m/s, and leaves at a point 5 m below the turbine inlet at atmospheric pressure and a velocity of 360 m/s. The turbine delivers shaft work at a rate of 70 kw, and the heat loss from the trubine is estimated to be 10 4 kcal/h. Calculate the specific enthalpy change associated with the process. 18

19 CBE14, Levicky 19

20 CBE14, Levicky Example Saturated steam at 1 atm is discharged from a turbine at a rate of 1150 kg/h. Superheated steam at 300 o C and 1 atm is needed as a feed to a heat exchanger; to produce it, the turbine discharge stream is mixed with superheated steam available from a second source at 400 o C and 1 atm, such that the product is superheated steam at 300 o C and 1 atm. The mixing unit operates adiabatically. Calculate the amount of superheated steam at 300 o C produced and the required volumetric flow rate of the 400 o C steam. 0

21 CBE14, Levicky 1

22 CBE14, Levicky Mechanical Energy Balance and The Bernoulli Equation The general energy balance derived previously can be recast into a mechanical energy balance. The mechanical energy balance is most useful for processes in which changes in the potential and kinetic energies are of primary interest, rather than changes in internal energy or heat associated with the process. Thus the mechanical energy balance is mainly used for purely-mechanical flow problems - i.e. problems in which heat transfer, chemical reactions, or phase changes are not present. We start from equation 1, in which we have reverted from specific enthalpy notation back to internal energy and PV work using Ĥ = Uˆ + P Vˆ, de dt k dep du + + = dt dt m& Uˆ input streams u + PVˆ + + gz output streams m& Uˆ + P Vˆ u + + gz + Q& W& s Now we make several additional assumptions. First, we assume steady state, so that all terms on the left hand side become zero. Second, we assume that the system has only a single inlet and a single outlet. Moreover, steady state implies that the inlet mass flowrate must equal the outlet mass flowrate, in order to avoid accumulation of material in the system. These adustments lead to uin uout 0 = m& ( Uˆ in + Pin Vˆ in + + gzin Uˆ out Pout Vˆ out gzout ) + Q& W& s (14) In the above equation, subscript "in" refers to the inlet port, and subscript "out" to the outlet port. Next, we divide the entire equation by m&, and write specific volume (volume/mass) as Vˆ = 1/ρ, where ρ is the density (mass/volume) of the flowing material. Moreover, we assume that the flow is incompressible, so that density is constant. A constant density means that Vˆ in = Vˆ out = 1/ρ. Also, we define Uˆ = Uˆ out - Uˆ in, P = P out - P in, etc. With these changes, equation 14 becomes Q& P u ( Uˆ ) + + m& ρ The term ( U Q& m& ) W& + g z = m& s ˆ in the absence of chemical reactions, phase changes, or other sources of large amounts of heat transfer; i.e. under typical conditions of (15)

23 CBE14, Levicky usage for the mechanical balance equation will mostly represent heat generated due to the viscous friction in the fluid. In such situations, this term is called the friction loss and we will write it as Fˆ. With this last change, equation 15 assumes the usual form of the mechanical energy balance, P u + ρ + g z + Fˆ = W& m& s (16) & Note that m W s & is the shaft work performed by the system on the surroundings, per unit mass of material passing through the system. In many instances, the amount of energy lost to viscous dissipation in the fluid is small compared to magnitudes of the other terms in equation 16. In such a case, Fˆ 0. Moreover, many common flows (e.g. fluid flow through a pipe; what is the system in this case?) do not have any appreciable shaft work associated with them, so that & m& W s = 0. For such inviscid (i.e. frictionless) flows with no shaft work, the mechanical energy balance simplifies to Bernoulli s equation: P u + ρ + g z = 0 (17) Bernoulli s equation has a wide range of application, despite its simplifying assumptions. Finally, it is often necessary to relate the volumetric flowrate V & or the mass flowrate m& through a pipe or other conduit to the average fluid velocity u. The relations are V & = Au (18) m& = V & ρ = ρau (19) In equations 18 and 19 A is the cross-sectional area of the flow. Example Water flows from an elevated reservoir through a conduit to a turbine at a lower level and out of the turbine through a similar conduit. Note that 3

24 CBE14, Levicky the cross-sectional area of the conduits is constant. At a point 100 m above the turbine the pressure is 07 kpa, and at a point 3 m below the turbine the pressure is 14 kpa. What must the water flow rate be if the turbine output is 1.00 MW? Do we need to make any additional assumptions in order to solve this problem? 4

### Chapter 6 Energy Equation for a Control Volume

Chapter 6 Energy Equation for a Control Volume Conservation of Mass and the Control Volume Closed systems: The mass of the system remain constant during a process. Control volumes: Mass can cross the boundaries,

### The First Law of Thermodynamics

The First Law of Thermodynamics (FL) The First Law of Thermodynamics Explain and manipulate the first law Write the integral and differential forms of the first law Describe the physical meaning of each

### k is change in kinetic energy and E

Energy Balances on Closed Systems A system is closed if mass does not cross the system boundary during the period of time covered by energy balance. Energy balance for a closed system written between two

### Basic Concepts of Thermodynamics

Basic Concepts of Thermodynamics Every science has its own unique vocabulary associated with it. recise definition of basic concepts forms a sound foundation for development of a science and prevents possible

### Mass and Energy Analysis of Control Volumes

MAE 320-Chapter 5 Mass and Energy Analysis of Control Volumes Objectives Develop the conservation of mass principle. Apply the conservation of mass principle to various systems including steady- and unsteady-flow

### The First Law of Thermodynamics: Closed Systems. Heat Transfer

The First Law of Thermodynamics: Closed Systems The first law of thermodynamics can be simply stated as follows: during an interaction between a system and its surroundings, the amount of energy gained

### AP2 Fluids. Kinetic Energy (A) stays the same stays the same (B) increases increases (C) stays the same increases (D) increases stays the same

A cart full of water travels horizontally on a frictionless track with initial velocity v. As shown in the diagram, in the back wall of the cart there is a small opening near the bottom of the wall that

### du u U 0 U dy y b 0 b

BASIC CONCEPTS/DEFINITIONS OF FLUID MECHANICS (by Marios M. Fyrillas) 1. Density (πυκνότητα) Symbol: 3 Units of measure: kg / m Equation: m ( m mass, V volume) V. Pressure (πίεση) Alternative definition:

### Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS

Fluid Mechanics: Fundamentals and Applications, 2nd Edition Yunus A. Cengel, John M. Cimbala McGraw-Hill, 2010 Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS Lecture slides by Hasan Hacışevki Copyright

### Final Exam Review Questions PHY Final Chapters

Final Exam Review Questions PHY 2425 - Final Chapters Section: 17 1 Topic: Thermal Equilibrium and Temperature Type: Numerical 12 A temperature of 14ºF is equivalent to A) 10ºC B) 7.77ºC C) 25.5ºC D) 26.7ºC

### THERMODYNAMICS NOTES - BOOK 2 OF 2

THERMODYNAMICS & FLUIDS (Thermodynamics level 1\Thermo & Fluids Module -Thermo Book 2-Contents-December 07.doc) UFMEQU-20-1 THERMODYNAMICS NOTES - BOOK 2 OF 2 Students must read through these notes and

### CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology

CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology The Continuum Hypothesis: We will regard macroscopic behavior of fluids as if the fluids are perfectly continuous in structure. In reality,

### 4.1 Introduction. 4.2 Work. Thermodynamics

Thermodynamics 4-1 Chapter 4 Thermodynamics 4.1 Introduction This chapter focusses on the turbine cycle:thermodynamics and heat engines. The objective is to provide enough understanding of the turbine

### Chapter 10 Temperature and Heat

Chapter 10 Temperature and Heat What are temperature and heat? Are they the same? What causes heat? What Is Temperature? How do we measure temperature? What are we actually measuring? Temperature and Its

### Practice Problems on Conservation of Energy. heat loss of 50,000 kj/hr. house maintained at 22 C

COE_10 A passive solar house that is losing heat to the outdoors at an average rate of 50,000 kj/hr is maintained at 22 C at all times during a winter night for 10 hr. The house is to be heated by 50 glass

### CO 2 41.2 MPa (abs) 20 C

comp_02 A CO 2 cartridge is used to propel a small rocket cart. Compressed CO 2, stored at a pressure of 41.2 MPa (abs) and a temperature of 20 C, is expanded through a smoothly contoured converging nozzle

### ENERGY CONSERVATION The First Law of Thermodynamics and the Work/Kinetic-Energy Theorem

PH-211 A. La Rosa ENERGY CONSERVATION The irst Law of Thermodynamics and the Work/Kinetic-Energy Theorem ENERGY TRANSER of ENERGY Heat-transfer Q Macroscopic external Work W done on a system ENERGY CONSERVATION

### FUNDAMENTALS OF ENGINEERING THERMODYNAMICS

FUNDAMENTALS OF ENGINEERING THERMODYNAMICS System: Quantity of matter (constant mass) or region in space (constant volume) chosen for study. Closed system: Can exchange energy but not mass; mass is constant

### CBE 6333, R. Levicky 1 Differential Balance Equations

CBE 6333, R. Levicky 1 Differential Balance Equations We have previously derived integral balances for mass, momentum, and energy for a control volume. The control volume was assumed to be some large object,

### 20 m neon m propane 20

Problems with solutions:. A -m 3 tank is filled with a gas at room temperature 0 C and pressure 00 Kpa. How much mass is there if the gas is a) Air b) Neon, or c) Propane? Given: T73K; P00KPa; M air 9;

### Heat as Energy Transfer. Heat is energy transferred from one object to another because of a difference in temperature

Unit of heat: calorie (cal) Heat as Energy Transfer Heat is energy transferred from one object to another because of a difference in temperature 1 cal is the amount of heat necessary to raise the temperature

### Physics Final Exam Chapter 13 Review

Physics 1401 - Final Exam Chapter 13 Review 11. The coefficient of linear expansion of steel is 12 10 6 /C. A railroad track is made of individual rails of steel 1.0 km in length. By what length would

### Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

### THERMOCHEMISTRY & DEFINITIONS

THERMOCHEMISTRY & DEFINITIONS Thermochemistry is the study of the study of relationships between chemistry and energy. All chemical changes and many physical changes involve exchange of energy with the

### Answer, Key Homework 6 David McIntyre 1

Answer, Key Homework 6 David McIntyre 1 This print-out should have 0 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making

### Lesson 5 Review of fundamental principles Thermodynamics : Part II

Lesson 5 Review of fundamental principles Thermodynamics : Part II Version ME, IIT Kharagpur .The specific objectives are to:. State principles of evaluating thermodynamic properties of pure substances

### The Equipartition Theorem

The Equipartition Theorem Degrees of freedom are associated with the kinetic energy of translations, rotation, vibration and the potential energy of vibrations. A result from classical statistical mechanics

### State Newton's second law of motion for a particle, defining carefully each term used.

5 Question 1. [Marks 28] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

### Chapter 3 Process Variables. Mass and Volume

Chapter 3 Process Variables Process: to a chemical engineer, the set of tasks or operations that accomplish a chemical or material transformation to produce a product Feed or inputs: raw materials and

### Sheet 5:Chapter 5 5 1C Name four physical quantities that are conserved and two quantities that are not conserved during a process.

Thermo 1 (MEP 261) Thermodynamics An Engineering Approach Yunus A. Cengel & Michael A. Boles 7 th Edition, McGraw-Hill Companies, ISBN-978-0-07-352932-5, 2008 Sheet 5:Chapter 5 5 1C Name four physical

### ME 305 Fluid Mechanics I. Part 4 Integral Formulation of Fluid Flow

ME 305 Fluid Mechanics I Part 4 Integral Formulation of Fluid Flow These presentations are prepared by Dr. Cüneyt Sert Mechanical Engineering Department Middle East Technical University Ankara, Turkey

### Chapter 28 Fluid Dynamics

Chapter 28 Fluid Dynamics 28.1 Ideal Fluids... 1 28.2 Velocity Vector Field... 1 28.3 Mass Continuity Equation... 3 28.4 Bernoulli s Principle... 4 28.5 Worked Examples: Bernoulli s Equation... 7 Example

### Example 1. Solution: Diagram: Given: m = 1 kg P 1 = P 2 = 0.8 MPa = constant v 1 = m 3 /kg v 2 = m 3 /kg. Find:

Example 1 Problem Statement: A piston/cylinder device contains one kilogram of a substance at 0.8 MPa with a specific volume of 0.2608 m 3 /kg. The substance undergoes an isobaric process until its specific

### Expansion and Compression of a Gas

Physics 6B - Winter 2011 Homework 4 Solutions Expansion and Compression of a Gas In an adiabatic process, there is no heat transferred to or from the system i.e. dq = 0. The first law of thermodynamics

### df dt df dt df ds df ds

Principles of Fluid Mechanics Fluid: Fluid is a substance that deforms or flows continuously under the action of a shear stress (force per unit area). In fluid mechanics the term fluid can refer to any

### Vapor-Liquid Equilibria

31 Introduction to Chemical Engineering Calculations Lecture 7. Vapor-Liquid Equilibria Vapor and Gas Vapor A substance that is below its critical temperature. Gas A substance that is above its critical

### Exam 4 -- PHYS 101. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Name: Class: Date: Exam 4 -- PHYS 101 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A steel tape measure is marked such that it gives accurate measurements

### High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur

High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 06 One-dimensional Gas Dynamics (Contd.) We

### Course 2 Mathematical Tools and Unit Conversion Used in Thermodynamic Problem Solving

Course Mathematical Tools and Unit Conversion Used in Thermodynamic Problem Solving 1 Basic Algebra Computations 1st degree equations - =0 Collect numerical values on one side and unknown to the otherside

### Entropy and The Second Law of Thermodynamics

The Second Law of Thermodynamics (SL) Entropy and The Second Law of Thermodynamics Explain and manipulate the second law State and illustrate by example the second law of thermodynamics Write both the

### Chapter 8 and 9 Energy Balances

Chapter 8 and 9 Energy Balances Reference States. Recall that enthalpy and internal energy are always defined relative to a reference state (Chapter 7). When solving energy balance problems, it is therefore

### Energy in Thermal Processes: The First Law of Thermodynamics

Energy in Thermal Processes: The First Law of Thermodynamics 1. An insulated container half full of room temperature water is shaken vigorously for two minutes. What happens to the temperature of the water?

### State Newton's second law of motion for a particle, defining carefully each term used.

5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding

### Chapter 18 Temperature, Heat, and the First Law of Thermodynamics. Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57

Chapter 18 Temperature, Heat, and the First Law of Thermodynamics Problems: 8, 11, 13, 17, 21, 27, 29, 37, 39, 41, 47, 51, 57 Thermodynamics study and application of thermal energy temperature quantity

### Macroscopic Balances for Nonisothermal Systems

Transport Phenomena Macroscopic Balances for Nonisothermal Systems 1 Macroscopic Balances for Nonisothermal Systems 1. The macroscopic energy balance 2. The macroscopic mechanical energy balance 3. Use

### The First Law of Thermodynamics

Thermodynamics The First Law of Thermodynamics Thermodynamic Processes (isobaric, isochoric, isothermal, adiabatic) Reversible and Irreversible Processes Heat Engines Refrigerators and Heat Pumps The Carnot

### Control of superheater for electrical steam boiler at Esbjerg power plant

Control of superheater for electrical steam boiler at Esbjerg power plant Period: November 1 st 2009 January 7 th 2010 Due date: January 7 th 2010 Student: Rasmus Holmgaard Rasmussen Supervisor: Zhenyu

### Practice Problems on Bernoulli s Equation. V car. Answer(s): p p p V. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Sep 15

bernoulli_0 A person holds their hand out of a car window while driving through still air at a speed of V car. What is the maximum pressure on the person s hand? V car 0 max car p p p V C. Wassgren, Purdue

### = 800 kg/m 3 (note that old units cancel out) 4.184 J 1000 g = 4184 J/kg o C

Units and Dimensions Basic properties such as length, mass, time and temperature that can be measured are called dimensions. Any quantity that can be measured has a value and a unit associated with it.

### This chapter deals with three equations commonly used in fluid mechanics:

MASS, BERNOULLI, AND ENERGY EQUATIONS CHAPTER 5 This chapter deals with three equations commonly used in fluid mechanics: the mass, Bernoulli, and energy equations. The mass equation is an expression of

### Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### Physics 2AB Notes - 2012. Heating and Cooling. The kinetic energy of a substance defines its temperature.

Physics 2AB Notes - 2012 Heating and Cooling Kinetic Theory All matter is made up of tiny, minute particles. These particles are in constant motion. The kinetic energy of a substance defines its temperature.

### 1. (Problem 8.23 in the Book)

1. (Problem 8.23 in the Book) SOLUTION Schematic An experimental nuclear core simulation apparatus consists of a long thin-walled metallic tube of diameter D and length L, which is electrically heated

### 1 Theoretical Background of PELTON Turbine

c [m/s] linear velocity of water jet u [m/s) runner speed at PCD P jet [W] power in the jet de kin P T [W] power of turbine F [N] force F = dj Q [m 3 /s] discharge, volume flow ρ [kg/m 3 ] density of water

### PSS 17.1: The Bermuda Triangle

Assignment 6 Consider 6.0 g of helium at 40_C in the form of a cube 40 cm. on each side. Suppose 2000 J of energy are transferred to this gas. (i) Determine the final pressure if the process is at constant

### Engineering Problem Solving as Model Building

Engineering Problem Solving as Model Building Part 1. How professors think about problem solving. Part 2. Mech2 and Brain-Full Crisis Part 1 How experts think about problem solving When we solve a problem

### 1.1 Thermodynamics and Energy

1.1 Thermodynamics and Energy What is Thermodynamics? Essentially, thermodynamics can be defined as the study of energy. Granted, this is a pretty broad definition, which suits it well, because thermodynamics

### (b) 1. Look up c p for air in Table A.6. c p = 1004 J/kg K 2. Use equation (1) and given and looked up values to find s 2 s 1.

Problem 1 Given: Air cooled where: T 1 = 858K, P 1 = P = 4.5 MPa gage, T = 15 o C = 88K Find: (a) Show process on a T-s diagram (b) Calculate change in specific entropy if air is an ideal gas (c) Evaluate

### HNRS 227 Fall 2008 Chapter 4. Do You Remember These? iclicker Question. iclicker Question. iclicker Question. iclicker Question

HNRS 227 Fall 2008 Chapter 4 Heat and Temperature presented by Prof. Geller Do You Remember These? Units of length, mass and time, and metric Prefixes Density and its units The Scientific Method Speed,

### Thermodynamics I Spring 1432/1433H (2011/2012H) Saturday, Wednesday 8:00am - 10:00am & Monday 8:00am - 9:00am MEP 261 Class ZA

Thermodynamics I Spring 1432/1433H (2011/2012H) Saturday, Wednesday 8:00am - 10:00am & Monday 8:00am - 9:00am MEP 261 Class ZA Dr. Walid A. Aissa Associate Professor, Mech. Engg. Dept. Faculty of Engineering

### ECH 4224L Unit Operations Lab I Thin Film Evaporator. Introduction. Objective

Introduction In this experiment, you will use thin-film evaporator (TFE) to separate a mixture of water and ethylene glycol (EG). In a TFE a mixture of two fluids runs down a heated inner wall of a cylindrical

### QUESTIONS THERMODYNAMICS PRACTICE PROBLEMS FOR NON-TECHNICAL MAJORS. Thermodynamic Properties

QUESTIONS THERMODYNAMICS PRACTICE PROBLEMS FOR NON-TECHNICAL MAJORS Thermodynamic Properties 1. If an object has a weight of 10 lbf on the moon, what would the same object weigh on Jupiter? ft ft -ft g

### Energy : ṁ (h i + ½V i 2 ) = ṁ(h e + ½V e 2 ) Due to high T take h from table A.7.1

6.33 In a jet engine a flow of air at 000 K, 00 kpa and 30 m/s enters a nozzle, as shown in Fig. P6.33, where the air exits at 850 K, 90 kpa. What is the exit velocity assuming no heat loss? C.V. nozzle.

### Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 20 Conservation Equations in Fluid Flow Part VIII Good morning. I welcome you all

### THE KINETIC THEORY OF GASES

Chapter 19: THE KINETIC THEORY OF GASES 1. Evidence that a gas consists mostly of empty space is the fact that: A. the density of a gas becomes much greater when it is liquefied B. gases exert pressure

### Thermodynamic Systems

Student Academic Learning Services Page 1 of 18 Thermodynamic Systems And Performance Measurement Contents Thermodynamic Systems... 2 Defining the System... 2 The First Law... 2 Thermodynamic Efficiency...

### Second Law of Thermodynamics

Thermodynamics T8 Second Law of Thermodynamics Learning Goal: To understand the implications of the second law of thermodynamics. The second law of thermodynamics explains the direction in which the thermodynamic

### 1.5. Which thermodynamic property is introduced using the zeroth law of thermodynamics?

CHAPTER INTRODUCTION AND BASIC PRINCIPLES. (Tutorial). Determine if the following properties of the system are intensive or extensive properties: Property Intensive Extensive Volume Density Conductivity

### Module 3. First law of thermodynamics

Module 3 First law of thermodynamics First Law of Thermodynamics Statement: When a closed system executes a complete cycle the sum of heat 1 B interactions is equal to the sum of work interactions. Y A

### Chapter 13 - Solutions

= Chapter 13 - Solutions Description: Find the weight of a cylindrical iron rod given its area and length and the density of iron. Part A On a part-time job you are asked to bring a cylindrical iron rod

### For Water to Move a driving force is needed

RECALL FIRST CLASS: Q K Head Difference Area Distance between Heads Q 0.01 cm 0.19 m 6cm 0.75cm 1 liter 86400sec 1.17 liter ~ 1 liter sec 0.63 m 1000cm 3 day day day constant head 0.4 m 0.1 m FINE SAND

### a) Use the following equation from the lecture notes: = ( 8.314 J K 1 mol 1) ( ) 10 L

hermodynamics: Examples for chapter 4. 1. One mole of nitrogen gas is allowed to expand from 0.5 to 10 L reversible and isothermal process at 300 K. Calculate the change in molar entropy using a the ideal

### Second Law of Thermodynamics Alternative Statements

Second Law of Thermodynamics Alternative Statements There is no simple statement that captures all aspects of the second law. Several alternative formulations of the second law are found in the technical

### APPLIED THERMODYNAMICS TUTORIAL 1 REVISION OF ISENTROPIC EFFICIENCY ADVANCED STEAM CYCLES

APPLIED THERMODYNAMICS TUTORIAL 1 REVISION OF ISENTROPIC EFFICIENCY ADVANCED STEAM CYCLES INTRODUCTION This tutorial is designed for students wishing to extend their knowledge of thermodynamics to a more

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### Gravitational Potential Energy

Gravitational Potential Energy Consider a ball falling from a height of y 0 =h to the floor at height y=0. A net force of gravity has been acting on the ball as it drops. So the total work done on the

### CBE 6333, R. Levicky 1. Potential Flow

CBE 6333, R. Levicky Part I. Theoretical Background. Potential Flow Potential Flow. Potential flow is irrotational flow. Irrotational flows are often characterized by negligible viscosity effects. Viscous

### Problems of Chapter 2

Section 2.1 Heat and Internal Energy Problems of Chapter 2 1- On his honeymoon James Joule traveled from England to Switzerland. He attempted to verify his idea of the interconvertibility of mechanical

### An introduction to thermodynamics applied to Organic Rankine Cycles

An introduction to thermodynamics applied to Organic Rankine Cycles By : Sylvain Quoilin PhD Student at the University of Liège November 2008 1 Definition of a few thermodynamic variables 1.1 Main thermodynamics

### ME 201 Thermodynamics

ME 0 Thermodynamics Second Law Practice Problems. Ideally, which fluid can do more work: air at 600 psia and 600 F or steam at 600 psia and 600 F The maximum work a substance can do is given by its availablity.

### ME 211 TERMODYNAMICS I

ME 211 TERMODYNAMICS I Prof. Dr. Haşmet Türkoğlu Asst. Prof. Dr. Ekin Özgirgin YAPICI Çankaya University Faculty of Engineering Mechanical Engineering Department Fall, 2016 1 CHAPTER 1: INTORDUCTION Thermodynamics

### Kinetic Theory of Gases

Kinetic Theory of Gases Important Points:. Assumptions: a) Every gas consists of extremely small particles called molecules. b) The molecules of a gas are identical, spherical, rigid and perfectly elastic

### FRANCIS TURBINE EXPERIMENT

FRANCIS TURBINE EXPERIMENT 1. OBJECT The purpose of this experiment is to study the constructional details and performance parameters of Francis Turbine. 2. INTRODUCTION Turbines are subdivided into impulse

### The Relationships Between. Internal Energy, Heat, Enthalpy, and Calorimetry

The Relationships Between Internal Energy, Heat, Enthalpy, and Calorimetry Recap of Last Class Last class, we began our discussion about energy changes that accompany chemical reactions Chapter 5 discusses:

### CENTRIFUGAL PUMP OVERVIEW Presented by Matt Prosoli Of Pumps Plus Inc.

CENTRIFUGAL PUMP OVERVIEW Presented by Matt Prosoli Of Pumps Plus Inc. 1 Centrifugal Pump- Definition Centrifugal Pump can be defined as a mechanical device used to transfer liquid of various types. As

### Forms of Energy. Freshman Seminar

Forms of Energy Freshman Seminar Energy Energy The ability & capacity to do work Energy can take many different forms Energy can be quantified Law of Conservation of energy In any change from one form

### PS-6.2 Explain the factors that determine potential and kinetic energy and the transformation of one to the other.

PS-6.1 Explain how the law of conservation of energy applies to the transformation of various forms of energy (including mechanical energy, electrical energy, chemical energy, light energy, sound energy,

### Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 7 Ideal Gas Laws, Different Processes Let us continue

### 3-1 Copyright Richard M. Felder, Lisa G. Bullard, and Michael D. Dickey (2014)

EQUATIONS OF STATE FOR GASES Questions A gas enters a reactor at a rate of 255 SCMH. What does that mean? An orifice meter mounted in a process gas line indicates a flow rate of 24 ft 3 /min. The gas temperature

### 34 Pascal s Principle, the Continuity Equation, and Bernoulli s Principle

34 Pascal s Principle, the Continuity Equation, and Bernoulli s Principle There are a couple of mistakes that tend to crop up with some regularity in the application of the Bernoulli equation P + rv +

### The Kinetic Theory of Gases Sections Covered in the Text: Chapter 18

The Kinetic Theory of Gases Sections Covered in the Text: Chapter 18 In Note 15 we reviewed macroscopic properties of matter, in particular, temperature and pressure. Here we see how the temperature and

### Kinetic Theory of Gases

Kinetic Theory of Gases Physics 1425 Lecture 31 Michael Fowler, UVa Bernoulli s Picture Daniel Bernoulli, in 1738, was the first to understand air pressure in terms of molecules he visualized them shooting

### Chapter 13 Gases. An Introduction to Chemistry by Mark Bishop

Chapter 13 Gases An Introduction to Chemistry by Mark Bishop Chapter Map Gas Gas Model Gases are composed of tiny, widely-spaced particles. For a typical gas, the average distance between particles is

### Transient Mass Transfer

Lecture T1 Transient Mass Transfer Up to now, we have considered either processes applied to closed systems or processes involving steady-state flows. In this lecture we turn our attention to transient

### = 1.038 atm. 760 mm Hg. = 0.989 atm. d. 767 torr = 767 mm Hg. = 1.01 atm

Chapter 13 Gases 1. Solids and liquids have essentially fixed volumes and are not able to be compressed easily. Gases have volumes that depend on their conditions, and can be compressed or expanded by

### Thermodynamics AP Physics B. Multiple Choice Questions

Thermodynamics AP Physics B Name Multiple Choice Questions 1. What is the name of the following statement: When two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium

### 11. IMPACT OF A JET. Introduction

11. IMPACT OF A JET Introduction Water turbines are widely used throughout the world to generate power. In the type of water turbine referred to as a Pelton wheel, one or more water jets are directed tangentially