10 litres of gas at atmospheric pressure is compressed isothermally to a volume of 1 litre and then allowed to expand adiabatically to 10 litres. (a) Sketch the processes on a pV diagram for a monatomic gas. (b) Make a similar sketch for a diatomic gas. (c) Is a net work done on or by the system? (d) Is it greater or less for the diatomic gas

The graph shown is for a dilute gas that follows the clockwise path of quasi-static steps: isobaric expansion, isochoric reduction of pressure, isobaric compression, and isochoric increase in pressure. The vertical axis is shown in multiples of the pressure pp, where p=2.5atm, and the horizontal axis is shown in multiples of V, where V=4L. Part (a)  What is the work done for the segment from state A to state B?  Part (b)  What is the work done for the segment from state B to state C?  Part (c)  What is the work done for the segment from state C to state D?  Part (d)  What is the total work done in making a single clockwise cycle, A to B to C to D?

Repeat the preceding calculations for an ideal diatomic gas expanding adiabatically from an initial volume of 0.500 m3 to a final volume of 1.25 m3, starting at a pressure of 1.01  105 Pa. (You must sketch the curve to find the work.) P2 =  W ≈

a) Consider a process involving an ideal diatomic gas with n = 3mol, following p = aV, where a = 1 x 105 Pa/m³ is a constant. The gas ex- pands from volume V; = 1 m³ to V; = 4m3. P2 Find the (i) work done on the gas. (ii) heat entering the gas. 1 (iii) change in the internal energy of the gas. b) Now consider the cycle depicted in the figure, involving the same amount of gas as in the previous part. A → B is the process described in the previous subtask, B → C an isochor and C → A an isobar. Additionally, V2/V1 = n = 4 and Vi = 1 m³. Find the Pi 3 i) work done by the gas during one loop of the cycle. V1 V2 V ii) thermal efficiency of the cycle. iii) maximum theoretical efficiency of a Car- not cycle having the same temperature extrema as in this cycle. iv) coefficient of performance of the cycle, if it were used as a refrigerator .