# Work In Thermodynamic Process

A piston is placed inside a cylindrical container, which has adiabatic walls. Initially, the piston divides the container into two equal parts, with volumes $$V$$ each, both containing an ideal gas $$G$$ at a pressure $$P$$. Then the piston is moved very slowly by an external force $$F_{ext}$$ till the volume on one side of the piston becomes thrice that on the other side.

Let the work done by $$F_{ext}$$ in doing so be $$W$$. $W=kPV$

If the heat capacity ratio of $$G$$ is $$\dfrac{5}{3}$$, then find $$k$$.

Note : Take the piston to be insulating.

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