Chapter 19 First Law of Thermodynamics

Transcription

1 Chapter 9 First Law o Thermodynamics When two bodies at dierent temperatures (T and T ) are placed in thermal contact, they ultimately reach a common temperature (T ) somewhere between the two initial temperature (T <T <T or T >T >T ). We say that heat has lowed rom the hotter to the colder body. In the eighteenth century heat was belieed to be an inisible, massless luid called caloric. Howeer, the caloric theory ailed to explain the generation o heat by riction. Until the middle o the eighteenth century, the term heat and temperature had essentially the same meaning. The relationship between heat and internal energy is embodied in the irst law o thermodynamics. 9. Speciic Heat (I) Black was the irst person to realize the rise in temperature o a body could be used to determine the quality o heat absorbed by it. I a quality o heat Q produces a change in temperature T in a body, its heat capacity is deined as: heat capacity Q/ T A common used (non-si) unit o heat is calorie, which used to be deined as the quality o heat required to raise the temperature o g o water rom 4.5ºC to 5.5ºC. calorie 4.86 J The British thermal unit (BTU) is the quality o heat required to raise the temperature o lb o water rom 63ºF to 64ºF. BTU454*00/805. calorie055.8 J

2 9. Speciic Heat (II) The quality o heat Q required to produce a change in temperature T is proportional to the mass o the sample m, and to T. Qmc T, where c is called the speciic heat o the material. The SI unit o the speciic heat is J/kg K (although the unit cal/g K is oten used). Speciic heat is a property o a gien substance, whereas heat capacity reers to a gien sample o material. c m Q T 3 9. Speciic Heat (III) Molar speciic heat: It is sometimes conenient to work with the number o moles n o a substance rather than its mass. C Q n T C is the molar speciic heat, measured in J/mol K or (cal/mol K). Since nm/m, where M is the molecular mass, we hae CMc. 4

3 9. Speciic Heat (I) The Method o Mixtures The method o mixtures, irst employed by Black, is used to determine the inal equilibrium temperature. Since there is no heat exchanged with the surroundings, the heat transerred to the colder body is equal to the heat transerred rom the hotter body. Q + Q m c T 0 + m c Where T T -T and T T -T. T 0 5 Example 9. A steel ball o mass m80 g has an initial temperature T 00 ºC. It is immersed in m50 g o water in a copper cup o mass m300 g. The initial temperature o the water and cup is T0 ºC. Find the inal temperature when the system reaches the thermal equilibrium, where c450 (J/kg K), c490 (J/kg K), and c3385 (J/kg K). Solution: mc ( T T ) + ( mc + m3c3 )( T T ) 0 36( T T 00) + ( )( T 5.8 C 0) 0 6

4 9. Latent Heat (I) Black recognized that adding heat to a system does not always result in a change in its temperature. The temperature remains constant when a substance changes it phase --- or example icewater Latent Heat (II) Latent heat o usion L : rom solid to liquid. Latent heat o aporization L : rom liquid to apor. L Q m 8

5 Example 9. A -kg chuck o ice at -0 ºC is added to 5 kg o liquid water at 45ºC. What is the inal temperature o the system. Solution: T (45 T T 7.93 C ) The Mechanical Equialent o Heat: Joule s Experiment Mechanical energy can transer to heat which was demonstrated through Joule s experiment. Heat was identiied as another orm o energy. Heat is energy transerred between two bodies as a consequence o a temperature dierence between them. How to conert heat back to mechanical energy? 0

6 9.4 Work in Thermodynamics Thermodynamics is concerned with the work done by a system and the heat it exchanges with its surrounding. Heat reseroir: a extremely large heat capacity. Quasistatic: The thermodynamic aluables (P,, T, n, etc.) o the system and its surroundings change ininitely slowly. Thus the system is always arbitrarily close to an equilibrium state. The work done by the gas is dw Fdx PAdx Pd W i Pd 9.4 Work in Thermodynamics: Quasistatic Quasistatic: The thermodynamic aluables (P,, T, n, etc.) o the system and its surroundings change ininitely slowly. Thus the system is always arbitrarily close to an equilibrium state.

7 9.4 Work in Thermodynamics: Isobaric Work In an isobaric process the expansion or compression occurs at constant pressure. W i Pd P ( i ) The work done by a system depends on the details o the process that takes it rom one equilibrium state to another (nonconseratie orce) Work in Thermodynamics: Isothermal Work In an isothermal process, the system is kept in contact with a single reseroir at temperature T. W i Pd nrt d i nrt ln( ) i 4

8 9.5 First Law o Thermodynamics The internal energy U is a state unction --- one that depends only on the thermodynamic state o the system. The change in internal energy o the system is U Q W In this deinition, Q is positie when heat enters the system and W is positie when work is done by the system on its surroundings. * Notice that we can speciy only the change in internal energy. The irst law o thermodynamics is a generalization o the results o many experiments, starting with those o Mayer and Joule. It seres as a general deinition o heat First Law o Thermodynamics (II) The internal energy U is the sum o all possible kinds o energy stored in the system --- mechanical, electrical, magnetic, chemical, nuclear, and so on. It does not include the kinetic and potential energies associated with the center o mass o the system. The kinetic and potential energies associated with the random notion o particles orm a part o internal energy called thermal energy. Where would the heat come rom? Does a heat reseroir posses a large quantity o heat? 6

9 9.5 First Law o Thermodynamics (III) The physical quantity possessed by a system is internal energy, which is the sum o all the kinds o energy in the system. The internal energy is a state unction that depends on the equilibrium state o a system, whereas Q and W depend on the thermodynamic path between two equilibrium states. That is, Q and W are associated with processes. The heat absorbed by a system will increase its internal energy, only some o which is thermal energy. How is it possible or heat to enter or to leae a system and yet not to be store in it? Sound energy enters and leaes your bodies, but at any gien moment there is no sound stored Application o The First Law o Thermodynamics (a) Isolated System There is no heat exchange (Q0) and no work done on the external enironment (W0). U 0 or U constant The internal energy o an isolated system is constant. 8

10 9.6 Application o The First Law o Thermodynamics (b) Cyclic Process Energies operate in cycles, in which the system --- or example, a gas --- periodically returns to its initial state. Since the system returns to its initial state, the change in the internal energy in one complete cycle is zero; that is, U0. From the irst law we see that Q W Application o The First Law o Thermodynamics (c) Constant-olume Process In a constant-olume process, the olume o the system stays constant. Consequently, W0. From the irst law we see that U Q 0

11 9.6 Application o The First Law o Thermodynamics (d) Adiabatic Process In an adiabatic process, the system does not change heat with its surrounding; that is, Q0. From the irst law we see that U W In an adiabatic expansion the internal energy decreases. That is usually maniested as a drop in temperature. Conersely, when a gas is compressed adiabatically, its internal energy increases and the temperature rises. 9.6 Application o The First Law o Thermodynamics (e) Adiabatic Free Expansion What happens when a gas is allowed to expand adiabatically without doing work? Q 0 and W 0 U 0 This uncontrolled expansion is not quasistatic and cannot be depicted on a P diagram. In an adiabatic ree expansion, the internal energy does not change.

12 Example 9.4 A cylinder with a piston contains 0. kg o water at 00 ºC. What is the change in internal energy o the water when it is conerted to steam at 00 ºC at a constant pressure? The density o the water ρ w 000 kg/m 3 and that o steam is ρ s 0.6 kg/m 3. The Latent heat o aporization o water is L.6x0 6 J/kg. Solution: Heat Q ml Work W P( s w) The change in internal energy is U Q W 48 kj J 5 J Ideal Gases: Speciic Heat Heat absorbed at constant olume is Since the work done by the gas is zero, we see that Q U nc Q T nc T Heat absorbed at constant pressure is Q P nc P T The work done by the gas at constant pressure WP nc T nc P At ixed pressure P nr T, so the dierence between the two speciic heats is ( C P n( C C P P ) R T P C ) T 4

13 9.7 Ideal Gases: Adiabatic Quasistatic Process In an adiabatic process there is no heat exchange with the surroundings, so dq0. The work done by the gas or an ininitesimal change in olume d is dwpd. U nc W dt Pd From the equation o state or an ideal gas, PnRT, we hae nrdt Pd + dp (9.6) (9.7) Substituting Eq. 9.6 into Eq. 9.7, and rearranging it, we ind P( C + R) d + C dp Ideal Gases: Adiabatic Quasistatic Process With the deinition we hae which iners γ C / C P d γ γ P dp + P This equation applies to a quasistatic adiabatic process inoling an ideal gas. 0 constant The slop o the adiabatic cure is steeper than that o an isothermal cure. 6

14 Example 9.5 An ideal monatonic gas, or which γ5/3, undergoes a quasistatic expansion to one-third o its initial pressure. Find the ratio o the inal olume to the initial olume i the process is (a) isothermal; (b) adiabatic. Solution: (a) isothermal P constant. i (b) adiabatic i Pi P Pi ( P 3 ) γ 3 P 3/5 γ.9 constant 7 Example 9.6 Find the work done by an ideal gas when its state change adiabatically (a) rom P and to P and, and (b) rom T to T. Solution: W Pd (a) adiabatic ( P, ) - - > ( P, ) W Pd (b) adiabatic rom T to T d K γ K ( γ γ γ ) ( γ P P ) W nc T c T dt nc ( T T ) 8

15 9.9 Heat Transport Heat transer occurs by three mechanisms:. In conduction heat is transerred by collisions between molecules, and in case o metal, by ree electrons.. In conection heat transport is associated with moement o warm and cold parts o a luid. 3. Radiation is the transer o energy without interening medium. A warm body radiates to its cooler surrounding Heat Transport: Conduction The rate o transer o heat through conduction, dq/dt, is proportional to the cross-section area, A, and to the temperature gradient, dt/dx. dq dt κa dt dx The constant κ, called the thermal conductiity, is a measure o the ability o a material to conduct heat. What is the thermal resistance? 30

16 9.9 Heat Transport: Conection A glider can gain altitude by entering a rising column o warm air called a thermal. 3 Exercises and Problems Ch.9: Ex. 3, 4, 3, 36, 43, 45, 50 Prob. 3, 8, 9 3