Thermodynamics

One mole of an ideal monoatomic gas undergoes two reversible processes $(\mathrm{A} \rightarrow \mathrm{B}$ and $\mathrm{B} \rightarrow \mathrm{C})$ as shown in the given figure:




$\mathrm{A} \rightarrow \mathrm{B}$ is an adiabatic process. If the total heat absorbed in the entire process $(\mathrm{A} \rightarrow \mathrm{B}$ and $\mathrm{B} \rightarrow \mathrm{C})$ is $\mathrm{R} T_2 \ln 10$, the value of $2 \log V_3$ is _______.


[Use, molar heat capacity of the gas at constant pressure, $C_{\mathrm{p}, \mathrm{m}}=\frac{5}{2} \mathrm{R}$ ]