Two identical, insulated pistons and cylinders each contain 10 moles of the same gas. The gases initially are at the same temperature and 2 bar pressure. They are both compressed to one-tenth of their original volumes. Piston/cylinder A was compressed reversibly and piston/cylinder B was compressed irreversibly. Which is at the higher final pressure?

here, we have two insulated piston cylinder assemblies. Both have same initial and final state properties. But, one is compressed reversibly while other is compresses irreversibly. Since, the reversible work is greater than the reversible work. Therefore:

(Work)B > (Work)A

Now, from first law of thermodynamics, setting ΔQ to zero (due to insulation ,no heat transfer), we get:

ΔU = W

Therefore, from this equation we know that:

(ΔU)B > (ΔU)A

The internal energy of piston/cylinder B will also be greater than the internal energy of piston/cylinder A. Assuming the gas to be ideal we know that internal energy is the function of temperature of gas only. Therefore, by this relation:

(T)B > (T)A

Thus, the temperature of B will be greater than that of A. Now, the volume is constant for both assemblies, thus we can apply Charles' Law.

(P)B/(T)B = (P)A/(T)A

(P)B = (P)A * (T)B/(T)A

It is clear from this equation that, for (T)B > (T)A, (P)B > (P)A

Therefore, the piston/cylinder B will be at higher pressure.