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Chapter 4: 4.9 (page 129)
Estimate the maximum possible COP of a household air conditioner. Use any reasonable values for the reservoir temperatures.
COP=21
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Use the definition of enthalpy to calculate the change in enthalpy between points 1 and 2 of the Rankine cycle, for the same numerical parameters as used in the text. Recalculate the efficiency using your corrected value of, and comment on the accuracy of the approximation.
Derive equation for the efficiency of the Otto cycle.
Suppose that heat leaks into your kitchen refrigerator at an average rate of 300 watts. Assuming ideal operation, how much power must it draw from the wall?
Prove directly (by calculating the heat taken in and the heat expelled) that a Carnot engine using an ideal gas as the working substance has an efficiency of
In an absorption refrigerator, the energy driving the process is supplied not as work, but as heat from a gas flame. (Such refrigerators commonly use propane as fuel, and are used in locations where electricity is unavailable.* ) Let us define the following symbols, all taken to be positive by definition:
Qf= heat input from flame
Qc= heat extracted from inside refrigerator
Qr= waste heat expelled to room
Tf= temperature of flame
Tc= temperature inside refrigerator
Tr= room temperature
(a) Explain why the "coefficient of performance" (COP) for an absorption refrigerator should be defined as Qc / Qf.
(b) What relation among Qf, Qc, and Qr is implied by energy conservation alone? Will energy conservation permit the COP to be greater than 1 ?
(c) Use the second law of thermodynamics to derive an upper limit on the COP, in terms of the temperatures Tf, Tc, and Tr alone.
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