Question

Two litres of an ideal gas at a pressure of 10 atm expands isothermally into a vacuum until its total volume is 10 litres. How much heat is absorbed and how much work is done in the expansion?

Answer 1

Heat absorbed for an isothermal expansion is given as, nRTln(V2V1) where, n is the number of moles,T is the constant temperature associated with the process, V2 is the final volume and V1 was the initial volume.

Considering, n=1 applying ideal gas law,we can find the temperature,

so,P1V1=nRT

or, T=P1V1nR

or, RT=P1V1 for,n=1

So,RT=10⋅2=20

So,heat absorbed is 1⋅20⋅ln(102)=32.2J

And we know,from 1 st law of thermodynamics,change in internal energy for an isothermal process is zero,so work done=heat absorbed=32.2J

HOPE IT HELPS!!!!