Lecture 30 - Chapter 6 Thermal & Energy Systems (Examples) 1

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1 Potential Energy ME 101: Thermal and Energy Systems Chapter 7 - Examples Gravitational Potential Energy U = mgδh Relative to a reference height Increase in elevation increases U Decrease in elevation decreases U Elastic Potential Energy U = 1 k( ΔL) Based upon the stored energy when the object is stretched or bent Based on Hooke s Law Always positive (compression or tension) 1 Kinetic Potential Energy U = mv Based upon the object s vibration, rotation, or translation Always positive 1 Work of a Force Power Rate at which work is performed P avg W = Δt Force moves the piston a distance Δd W = FΔd Dependent upon direction of force and distance Left picture, force is positive (F acts in same direction as piston s motion) Right picture, force is negative (F opposes the motion) 3 4 as Energy Temperature (T) is a measure of the average energy of motion (vibration) of molecules (Q) is a measure of the total energy of the system Energy in transit from one location to another because of a temperature difference ing Value (H) is the amount of energy released per unit mass of fuel that is burned Q = mh Specific (c) is the amount of heat required to change the temperature of a unit mass of material by one degree Q= mc( T T o ) Questions What is temperature? What is heat? What is heat transfer? 5 6 (Examples) 1

2 versus Temperature Temperature is a measure of the average energy of motion (vibration) of a molecule while heat is a measure of the total energy of a system Below, T 1 = T, but Q 1 <Q Transfer! T 1 Q 1 < Q T g is the form of energy that is transferred between two systems because of a temperature difference" 7 8 Transfer nd Law of Thermodynamics can only move from hot to cold, not vice-versa /Temperature Relation We can relate the change in heat (ΔQ) of an object to its change in temperature (ΔT) ΔQ = mcδt m is the mass of the object T HOT Transfer of! T COLD c is the specific heat (can be taken as a measure of the material s ability to store/transfer heat) 9 10 Specific! g Depends on the substance Specific Amount of heat per unit mass to raise temperature one degree Gold [19 J/kg K] Copper [387 J/kg K] Alcohol (ethyl) [400 J/kg K] Water [4186 J/kg K] 11 1 (Examples)

3 Example For example, to increase the temperature by 5 C of a 1 kg block of gold (with c = 19 J/kg K) initially at room temperature (15 C) will require a heat input of or about 0.6 BTUs or 150 calories ΔQ = ( 1kg)(19J/kg K)(5 K) = 645J Modes of Transfer! g Conduction" g Convection" g Radiation" Conduction! Conduction! g Transfer of energy from more energetic particles to adjacent less energetic particles as a result of interactions between particles" Wall Cola Air T 1! T! Q Fourier s Law of Conduction! cond ΔT = kt A (W) g k t - thermal conductivity" g ΔT - temperature gradient" Wall Cola Air T 1! T! Some Thermal Conductivity Values Silver [406 W/m K] Aluminum [05 W/m K] Fiberglass [0.04 W/m K] Wool Felt [0.04 W/m K] Air at 0 C [0.05 W/m K] Styrofoam [0.01 W/m K] (Examples) 3

4 Firewalking! Firewalkers are not actually firewalkers. They are really coalwalkers. The fire is lit well ahead of time to allow the wood to burn down to non-flaming coals. The event is always held at night. If it were done during daylight, the bed of coals would look instead like a bed of ashes. There is always a layer of ash covering the coals. By doing it at night, the glowing red light is still visible through this layer of ash. The firewalker never dawdles. Now, no selfrespecting firewalker would run across the coals -- that would be undignified. But firewalkers certainly are walking briskly. You never see firewalkers standing on the coals. g Mode of energy transfer between a solid and the adjacent liquid or gas that is in motion" g Combined effects of conduction and fluid motion" 19 0 Wind Chill is Real! q = ha( Ts T ) J / s h is the convection heat-transfer coefficient A is the surface area exchanging heat with the fluid T S is the surface temperature T is the fluid temperature 1 Forced and Free (Natural) Sinks sinks increase convective heat transfer by increasing both A and h Convection Process h [W/(m C)] Free -5 Forced (Examples) 4

5 Radiation! Radiation! g Energy emitted by matter in the form of electromagnetic waves as a result of changes in the electronic configurations of molecules" In a kitchen oven, what is the difference between the bake setting and the broil setting? 5 6 Conduction Qcond ΔT = ka L (Watts or Btu/hr) k is the thermal conductivity of the material A is the cross-sectional area of rod L is the length of the rod T is the change in temperature Convection Q = ha( T T ) in Watts or Btu conv s f h is the convection heat-transfer coefficient A is the surface area exchanging heat with the fluid T s is the surface temperature T f is the fluid temperature Natural Convection: Result of buoyancy forces of fluid Forced Convection: Fluid or object is in motion 7 8 Radiation 4 4 ( air ) Q = εσ A T T rad (W) Infrared waves transfer energy through air or vacuum ε is the emissivity of the material(between 0 and 1) σ is the Stefan-Boltzmann constant A is the surface area of the object T is the surface temperature of the object T air is the air temperature 9 (Examples) 5

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