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

$\mathrm{A}\to \mathrm{B}$ is an adiabatic process. If the total heat absorbed in the entire process $(\mathrm{A}\to \mathrm{B}$ and $\mathrm{B}\to \mathrm{C})$ is ${\mathrm{RT}}_2\ln 10$, the value of $2{\mathrm{logV}}_3$ is
[Use molar heat capacity of the gas at constant pressure, ${\mathrm{C}}_{\mathrm{p},\mathrm{m}}=\frac{5}{2}\mathrm{R}$]

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.