By performing a work W, an ideal gas is allowed to expand adiabatically and then keeping the volume constant, a heat Q is supplied to the gas to bring it to the initial pressure. Find the U2−U1, where the U1 & U2 are the initial and the final internal energies.

From First Law of ThermodynamicsΔQ=ΔU+ΔWLet initial internal energy be U.For 1st case :No heat is added and thus internal energy is used to do the work.⇒0=U−U1+W…(i)For 2nd case :Heat supplied is used only in increasing internal energy since no work is done due to constant volume.⇒Q=U2−U+0… (ii) From (i) and (ii), we getQ=U2−U1+W⇒U2−U1=Q−W