An ideal gas is taken through a cyclic process $1 \to 2 \to 3 \to 1 .$ At 1 temperature is $127^{0} C$ and volume is ${20cm}^{3}$ , while at 3 temperature is $27^{0} C$ and volume is ${50 cm}^{3}$ . The gas attains a state S in the process $3 \to 1$ where the pressure is same as at 2, then

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The volume of the gas at S is nearly ${23.1 cm}^{3}$

Net work done by the gas in cyclic process is positive

Work done by the gas in process $1 \to 2$ is negative

The volume of the gas at S is nearly ${41.2cm}^{3}$

answer is B, C.

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Detailed Solution

The P-V graph of the process is shown.

Equation of the process $3 \to 1$

$V = - \frac{3}{10} T + 140 \Rightarrow V = - \frac{3}{10} (\frac{P V}{n R}) + 140$

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