Thermal Behavior of Matter and Heat Engines - Department of ...

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When we stated the second law of thermodynamics, we said that the spontaneous flow of heat is always from high temperature to low temperature. The key word here is “spontaneous”. It is possible for heat to flow “uphill”, from a cold object to a hot one, but it doesn’t happen spontaneously - work must be done on the system to make it happen, just as work must be done to pump water from a well. Refrigerators, air conditioners, heat pumps are devices that use work to make heat flow against its natural tendency. By energy conservation, we have Q = Q W . h c + We define the coefficient of performance, COP, for a refrigerator as an indicator of its effectiveness: Qc COP = . W Typical values for COP are in the range 2 to 6. A heat pump can be considered as an air conditioner with the reservoirs switched. A heat pump does a work W to remove an amount of heat from the cold reservoir of outdoor air, then exhausts a heat Q h into the hot reservoir of air in the room. Just as with the refrigerator and the air conditioner, the heat going to the hot reservoir is Q = Q W . h c + In an ideal, reversible heat pump, we have Q c T = c holds, just as it does for a heat engine. Thus, if you want to add a heat Q h to a room, the work that must be done to accomplish this is ⎛ Q ⎞ ⎛ ⎞ = − = ⎜ − c T ⎟ = ⎜ − c W Q ⎟ h Qc Qh 1 Qh 1 . ⎝ Qh ⎠ ⎝ Th ⎠ Example An ideal heat pump, one that satisfies the Carnot relation, is used to heat a room that is at 293 K. If the pump does 275 J of work, how much heat does it supply to the room if the outdoor temperature is (a) 273 K or (b) 263 K? Q h T h 18
Answer: (a) Since W ⎛ T ⎞ = ⎜ − c Q ⎟ h 1 , we have ⎝ Th ⎠ W 275 J Qh = = = 4030 J . ⎛ Tc ⎞ ⎛ 273 K ⎞ ⎜1 − 1 T ⎟ ⎜ − h 293 K ⎟ ⎝ ⎠ ⎝ ⎠ (b) Similarly, we have W 275 J Qh = = = 2690 J . ⎛ Tc ⎞ ⎛ 263K ⎞ ⎜1 − 1 T ⎟ ⎜ − h 293K ⎟ ⎝ ⎠ ⎝ ⎠ As one might expect, the same amount of work provides less heat when the outside temperature is lower. That is, more work must be done on a colder day to provide the same heat to the inside air. 19
Page 1 and 2: Unit 11 Thermal Behavior of Matter
Page 3 and 4: pipelines typically include loops t
Page 5 and 6: Answer: The change in temperature
Page 7 and 8: Example The heat capacity of 1.00 k
Page 9 and 10: 11.5 Latent heats The latent heat,
Page 11 and 12: Substance Thermal conductivity, k,
Page 13 and 14: Q c ⎛ ∆T ⎞ = kc A⎜ ⎟t ⎝
Page 15 and 16: 11.7 Radiation All objects give off
Page 17: In addition, though not shown in th

Thermal Behavior of Matter and Heat Engines - Department of ...

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