Question on expansion and Compression of gas?

[PRAJOL]

Homework Statement

If a pressure of gas is suddenly reduced and we let the gas to expand again until it reaches equilibrium. What is final volume, work done and heat in this process? and what would be change in internal energy?
Again the pressure is suddenly increased back to initial pressure and gas is compressed to initial volume. What would be work done heat and change in internal energy?
Temperature is same throughout all process

Homework Equations

PV=nRT
ΔU=q+w
w=p*ΔV

The Attempt at a Solution

Here All the process is done at isothermal condition so Boyles law apply
P1V1=P2V2

where V2 is volume after the gas comes to equilibrium, so,
V2=P1V1/P2

since the process is carried in isothermal condition
ΔU=0

w=p*ΔV

0=q+p*ΔV -------> q=-p*ΔV

Now when the pressure is increased back to initial condition

ΔU=0 ( since process is still isothermal)
ΔU=q+p*ΔV ---------> q=-p*ΔV, here change in volume is volume after decreasing pressure - initial volume

I am not sure if I am correct or not? Help

 

[PRAJOL]

Can anyone help me with this problem?