Question

$n$ moles of a gas filled in a container at temperature $T$ is in thermodynamic equilibrium initially. If the gas is compressed slowly and isothermally to half its initial volume then the work done by the atmosphere on the piston is -

• A. $nRT\ln 2$
• B. $\frac{nRT}{2}$
• C. $-\frac{3nRT}{2}$
• D. $\frac{3nRT\ln 2}{2}$

Answer 1

The correct option is B $\frac{nRT}{2}$

In this case atmospheric pressure is constant,
which is equal to $P_{atm}$
Work done by atmosphere on piston during this process is $W=P_{atm}\Delta V=P_{atm}(V_i-V_f)=\frac{P_{atm}{V}_i}{2}$

Now initially $P_{gas}=P_{atm}$
From ideal gas equation
$P_{atm}{V}_i=nRT$

Hence ,$W=\frac{nRT}{2}$