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Chapter 4: Q. 4.12 (page 129)

Explain why a rectangular PVcycle, as considered in Problems 1.34 and 4.1, cannot be used (in reverse) for refrigeration.

Short Answer

Expert verified

The rectangular PV cycle doesn't show the property of The range of temperature at which working substance absorbs heat must be less than the range off temperature at which working substance rejects heat. Therefore it cannot be used for refrigeration.

Step by step solution

01

Concept Introduction

For cyclic process, PV diagram is a closed loop. The area of the PV diagram represents the amount of work done during the process.

02

Explanation

The range of temperature at which working substance absorbs heat must be less than the range off temperature at which working substance rejects heat. Since the rectangular PV cycle doesn't show this property, therefore it cannot be used for refrigeration.

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Most popular questions from this chapter

The ingenious Stirling engine is a true heat engine that absorbs heat from an external source. The working substance can be air or any other gas. The engine consists of two cylinders with pistons, one in thermal contact with each reservoir (see Figure 4.7). The pistons are connected to a crankshaft in a complicated way that we'll ignore and let the engineers worry about. Between the two cylinders is a passageway where the gas flows past a regenerator: a temporary heat reservoir, typically made of wire mesh, whose temperature varies

gradually from the hot side to the cold side. The heat capacity of the regenerator is very large, so its temperature is affected very little by the gas flowing past. The four steps of the engine's (idealized) cycle are as follows:
i. Power stroke. While in the hot cylinder at temperature Th, the gas absorbs heat and expands isothermally, pushing the hot piston outward. The piston in the cold cylinder remains at rest, all the way inward as shown in the figure.
ii. Transfer to the cold cylinder. The hot piston moves in while the cold piston moves out, transferring the gas to the cold cylinder at constant volume. While on its way, the gas flows past the regenerator, giving up heat and cooling to Tc.
iii. Compression stroke. The cold piston moves in, isothermally compressing the gas back to its original volume as the gas gives up heat to the cold reservoir. The hot piston remains at rest, all the way in.
iv. Transfer to hot cylinder. The cold piston moves the rest of the way in while the hot piston moves out, transferring the gas back to the hot cylinder at constant volume. While on its way, the gas flows past the regenerator, absorbing heat until it is again at Th.

(a) Draw a PV diagram for this idealized Stirling cycle.
(b) Forget about the regenerator for the moment. Then, during step 2, the gas will give up heat to the cold reservoir instead of to the regenerator; during step 4 , the gas will absorb heat from the hot reservoir. Calculate the efficiency of the engine in this case, assuming that the gas is ideal. Express your answer in terms of the temperature ratio Tc / Th and the compression ratio (the ratio of the maximum and minimum volumes). Show that the efficiency is less than that of a Carnot engine operating between the same temperatures. Work out a numerical example.
(c) Now put the regenerator back. Argue that, if it works perfectly, the efficiency of a Stirling engine is the same as that of a Carnot engine.
(d) Discuss, in some detail, the various advantages and disadvantages of a Stirling engine, compared to other engines.

Prove that if you had a heat engine whose efficiency was better than the ideal value (4.5), you could hook it up to an ordinary Carnot refrigerator to make a refrigerator that requires no work input.

In table 4.1, why does the entropy of water increase with increasing temperature, while the entropy of steam decreases with increasing temperature?

Suppose you are told to design a household air conditioner using

HFC-134a as its working substance. Over what range of pressures would you have it operate? Explain your reasoning. Calculate the COP for your design, and compare to the COP of an ideal Carnot refrigerator operating between the same extreme temperatures.

The amount of work done by each stroke of an automobile engine is controlled by the amount of fuel injected into the cylinder: the more fuel, the higher the temperature and pressure at points 3 and 4 in the cycle. But according to equation 4.10, the efficiency of the cycle depends only on the compression ratio (which is always the same for any particular engine), not on the amount of fuel consumed. Do you think this conclusion still holds when various other effects such as friction are taken into account? Would you expect a real engine to be most efficient when operating at high power or at low power? Explain.
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