Consider a thermodynamic cycle in a PV diagram shown in the figure performed by one mole of a monoatomic gas. The temperature at A is $T_{0}$ and volume at A and B are related as $V_{B} = V_{C} = 2 V_{A} .$ Choose the correct option(s) from the following

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Molar specific heat capacity of the process AB is 2R

Molar specific heat capacity of process AB is 3R

Net work done by the gas during the cycle is $0.5 R T_{0}$

The maximum temperature during the cycle is $4 T_{0}$

answer is A, B, C.

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Detailed Solution

Temperature at state ‘B’ is maximum
$\begin{array}{l} n R T_{B} = P_{B} V_{B} \\ n R T_{A} = P_{A} V_{A} \\ T_{B} = 4 T_{A} = 4 T_{0} \end{array}$
Net work done by gas in cyclic process
$(1) \frac{R}{2} (T_{B} - T_{A}) - (1) R (T_{C} - T_{A})$
$\frac{R}{2} 3 T_{0} - R T_{0} = 0.5 R T_{0}$
Heat capacity for process AB = $\frac{3 R}{2} + \frac{R}{2} = 2 R$