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Question

Helium gas goes through a cycle $$ABC$$ (consisting of two isochoric and isobaric lines) as shown in figure. Efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)
40181.PNG


A
15.4%
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B
9.1%
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C
10.5%
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D
12.5%
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Solution

The correct option is A $$15.4\% $$
$$\displaystyle \eta= \frac{Work \ done \ by \ gas}{Heat \ given \ to \  gas}$$

Work done by gas = Area under curve= $$P_0V_0$$
Heat given by gas= Heat given by gas from $$A$$ to $$B$$ + Heat given by gas from $$B$$ to $$C$$ 

Heat given by gas= $$nC_v\Delta T$$ + $$nC_p\Delta T$$
$$C_p$$ and $$C_v$$ for monoatomic gas is $$\dfrac{5R}{2}$$ and $$\dfrac{3R}{2}$$ respectively.
Heat given by gas= $$\dfrac{3}{2}P_0V_0$$ + $$5P_0V_0$$

$$\displaystyle \eta= \dfrac{P_0V_0}{\dfrac{3}{2}P_0V_0 + 5P_0V_0}= 15.4  %$$

Physics

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