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254.


Problem 26.27 (RHK)


One mole of an ideal monatomic gas is used as the working substance of an engine that operates on the cycle shown in the figure. We have to calculate (a) the work done by the engine per cycle; (b) the heat added per cycle during the expansion stroke abc; and (c) the engine efficiency. (d) We have to find the Carnot efficiency of an engine operating between the highest and lowest temperatures present in the cycle. We have to compare the Carnot efficiency with the efficiency calculated in (c). We may assume that , , , and




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(a) and (b)

Data of the problem are

and

The working substance of the engine is one mole of an ideal monatomic gas. Therefore, the ratio of its specific heats and

The process ab takes place at constant volume. Therefore, during this part of the process no work is done on the gas and an amount of heat which is equal to is absorbed. That is

During the part bc of the cycle, amount of work is done on the gas and amount of heat is absorbed by the gas. As the expansion of the gas takes place at constant pressure, we have

And

As,

Therefore, the amount of heat added per cycle during the expansion stroke abc will be

Let be the work done on the gas during compression from volume to at pressure .

Therefore, the total work done on the gas in each cycle will be

And therefore the total work done by the gas engine on the external system per cycle will be

(c)

The engine efficiency will be

That is the efficiency of the engine is 15.3%.

(d)

The highest temperature during the cycle will be at c,

The lowest temperature during the cycle will be at a,

Therefore, the Carnot efficiency of an engine operating between the highest and the lowest temperatures during the cycle will be

That is 75%.