Here, we have to find out the work done in an isothermal expansion of gas.
We have,
The work done by a gas when it expands by a very small volume, dV under a pressure, P.
dW = PdV
Hence, the total work done by a gas when the volume of one mole of gas increases from
V1 to
V2.
W =
PdV =
()dV [Since PV = RT
⇒ P =
]
Since, the temperature, T is a constant for an isothermal change,
W =
RT‌ =
RT[logeV]2VV1 =
RT(logeV2−logeV1) =
RTloge But,
P1V1 =
P2V2 = RT
∴ W =
P1V1loge() That is, the work done in an isothermal expansion of gas is given by
W =
P1V1loge