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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

A power plant produces1GWof electricity, at an efficiency of 40%(typical of today's coal-fired plants).

(a) At what rate does this plant expel waste heat into its environment?

(b) Assume first that the cold reservoir for this plant is a river whose flow rate is 100m3/s.By how much will the temperature of the river increase?

(c) To avoid this "thermal pollution" of the river, the plant could instead be cooled by evaporation of river water. (This is more expensive, but in some areas it is environmentally preferable.) At what rate must the water evaporate? What fraction of the river must be evaporated?

Why must you put an air conditioner in the window of a building, rather than in the middle of a room?

Calculate the efficiency of a Rankine cycle that is modified from the parameters used in the text in each of the following three ways (one at a time), and comment briefly on the results: (a) reduce the maximum temperature to 500°C; (b)reduce the maximum pressure to 100 bars; (c)reduce the minimum temperature to 10°C.

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.

Calculate the efficiency of a Rankine cycle that is modified from the parameters used in the text in each of the following three ways (one at a time), and comment briefly on the results:

(a) reduce the maximum temperature to 500oC;

(b) reduce the maximum pressure to 100 bars;

(c) reduce the minimum temperature to 10oC.
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