Which among the following gives the expression for work done by ideal gas?

Assume $\mathrm{n}$ moles of an ideal gas in a cylinder with a moveable, airtight, frictionless piston. Consider that the gas has a pressure $\mathrm{P}$ equal to the atmospheric pressure $\mathrm{P}$ outside. Let's say that the external pressure is decreased by an infinitesimally small amount, $\mathrm{dP}$, and concurrently the volume is slightly increased, dV.

In light of this, the minor tasks involved in the expansion process will be:

$dW=-Pext.dV; dW=-(P-dP)dV$

$\mathrm{dW}=-\mathrm{P}.\mathrm{dV}+\mathrm{dP}.\mathrm{dV}$

Due to the small values of $\mathrm{dP}$ and $\mathrm{dV}$, the product $\mathrm{dP}.\mathrm{dV}$ will be negligible in contrast to P.dV and can be disregarded.

$\therefore \mathrm{dW}=-\mathrm{P}.\mathrm{dV}$

The formula for work done in isothermal expansion is $-\mathrm{nRT}\ln {\mathrm{V}}_2/V_1$ which can also be written as $-2.303nRT\log V_2/V_1$                

Hence the correct option is (C).