Heat and Thermodynamics

The work done when a gas changes its volume at constant temperature (isothermal process) is given by:
W=nRT‌ln(‌

V2

V1

)
First Case: From V to 2V
We have n=2,V1=V, and V2=2V.
So, the work done is:
W=2RT‌ln(‌

2V

V

)=2RT‌ln(2)
Second Case: From 2V to 4V
Now, n=2,V1=2V, and V2=4V.
So, the work done here is:
‌W′=2RT‌ln(‌

4V

2V

)
‌=2RT‌ln(2)=W
The work done in increasing the volume from 2V to 4V is the same as the work done from V to 2V, both are W.