You need to design a heat engine that operates on a Brayton cycle and, during each cycle, does \(175 \mathrm{~J}\) of work while exhausting \(65 \mathrm{~J}\) of energy.

(a) If the working substance is helium gas, what should the pressure ratio be?

(b) If the working substance is carbon dioxide gas, \(\mathrm{CO}_{2}\), is the pressure ratio the same as with helium gas? If so, prove it; if not, determine the new pressure ratio.