c) A sample consisting of 200 mol He is cypunded isothermally at \( 22^{\circ} \mathrm{C} \) from \( 228 \mathrm{dm}^{3} \) to \( 31.7 \mathrm{dm}^{4} \) (i) reversibly, (i) against a constant extermal prevare equal to the final pressurc of the pas, and (iii) fresly (apainst zero external prowsurel. For the three procesess calculate \( \psi, \pi, \Delta V \), and \( \Delta I \), ( 5 marks)
d) Calculate \( \Delta S \) (for the system) when the state of 200 mol diatomic perfect gas molecules, for which \( \mathrm{C}_{\mathrm{r}}=7=7 / 2 R \) is changed from \( 25^{\circ} \mathrm{C} \) and 1.50 atm to \( 135^{\circ} \mathrm{C} \) and 7.00 atm . 7 marks)