One mole of an ideal gas has an internal energy given by U = U_o + 2 PV, where P is the pressure and V the volume of the gas, U_o is a constant. this gas undergoes the quasi-static cyclic process ABCD as shown the U-V diagram. choose the correct statement (s) :

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The molar heat capacity of the gas at constant pressure is 3R

The gas must be monoatomic

The gas must be diatomic

The work done by the ideal gas in the process AB is $\frac{U_{1} - U_{0}}{2} \ln 2$

answer is A, D.

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Detailed Solution

$W_{A \to B} = {nRT}_{1} \ln 2$
$\begin{array}{l} W_{A \to B} = \frac{U_{1} - U_{0}}{2} \ln 2 \\ \frac{d U}{dT} = 2 R \\ d U = 2 RdT \\ C_{V} = 2 R \\ C_{P} = 3 R \end{array}$

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