A thermally insulated cylinder having a frictionless piston contains \(\mathrm{N}_{2}\) gas. The piston is held in place by latches in such a way that it divides the cylinder into two equal halves. Each half of the cylinder contains \(30 \mathrm{~L}\) of \(\mathrm{N}_{2}\) gas at \(2 \mathrm{~atm}\) and \(25^{\circ} \mathrm{C}\). The restraining latches are removed and heat is supplied to the gas to the lower half of the cylinder until the piston compresses the gas on the upper half to \(4.5 \mathrm{~atm}\). Take \(C_{P}=29.10 \mathrm{~kJ} / \mathrm{kmol}-\mathrm{K}\) and \(C_{V}=20.78 \mathrm{~kJ} / \mathrm{mol}-\mathrm{K}\).

(i) Calculate the final temperature of the gas on the upper half.

(ii) Determine the work done on the gas on the upper half.

(iii) What is the final temperature of the gas on the lower half?

(iv) How much heat is supplied to the lower half of the cylinder?