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Chapter 4: Q. 4.37 (page 148)

A common (but imprecise) way of stating the third law of thermodynamics is "You can't reach absolute zero." Discuss how the third law, as stated in Section 3.2, puts limits on how low a temperature can be attained by various refrigeration techniques.

Short Answer

Expert verified

The refrigeration techniques cannot attain absolute zero temperature

Step by step solution

01

Given Information

Given techniques: refrigeration techniques

How low a temperature can be attained by various refrigeration techniques

02

Explanation

As per the Third law of thermodynamics, entropy of the system tends to zero at absolute zero temperature.

As entropy approaches zero at absolute zero temperature therefore the heat capacity also goes to zero. This means that the heat capacity becomes negligibly low at very low temperature.

So the cooling process becomes ineffective for very low heat capacity. This is the reason why refrigeration requires temperature higher than absolute zero.

So we can say that the refrigeration techniques cannot attain absolute zero temperature.

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Most popular questions from this chapter

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

Consider an ideal Hampson-Linde cycle in which no heat is lost to the environment.

(a) Argue that the combination of the throttling valve and the heat exchanger is a constant-enthalpy device, so that the total enthalpy of the fluid coming out of this combination is the same as the enthalpy of the fluid going in.

(b) Let xbe the fraction of the fluid that liquefies on each pass through the cycle. Show that

x=Hout-HinHout-Hliq,

where Hinis the enthalpy of each mole of compressed gas that goes into the heat exchanger, Houtis the enthalpy of each mole of low-pressure gas that comes out of the heat exchanger, and Hliqis the enthalpy of each mole of liquid produced.

(c) Use the data in Table 4.5to calculate the fraction of nitrogen liquefied on each pass through a Hampson-Linde cycle operating between 1 bar and 100 bars, with an input temperature of 300K. Assume that the heat exchanger works perfectly, so the temperature of the low-pressure gas coming out of it is the same as the temperature of the high-pressure gas going in. Repeat the calculation for an input temperature of 200K.

At a power plant that produces 1 GW109 watts) of electricity, the steam turbines take in steam at a temperature of 500o, and the waste heat is expelled into the environment at 20o
(a) What is the maximum possible efficiency of this plant?
(b) Suppose you develop a new material for making pipes and turbines, which allows the maximum steam temperature to be raised to 600o. Roughly how much money can you make in a year by installing your improved hardware, if you sell the additional electricity for 5 cents per kilowatt-hour? (Assume that the amount of fuel consumed at the plant is unchanged.)

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

Consider a household refrigerator that uses HFC-134a as the refrigerant, operating between the pressures of 1.0barand 10bars.

(a) The compression stage of the cycle begins with saturated vapor at 1 bar and ends at 10 bars. Assuming that the entropy is constant during compression, find the approximate temperature of the vapor after it is compressed. (You'll have to do an interpolation between the values given in Table 4.4.)

(b) Determine the enthalpy at each of the points 1,2,3 and 4 , and calculate the coefficient of performance. Compare to the COP of a Carnot refrigerator operating between the same extreme temperatures. Does this temperature range seem reasonable for a household refrigerator? Explain briefly.

(c) What fraction of the liquid vaporizes during the throttling step?
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