The graph in ?Fig. P19.36 shows a pV-diagram for 3.25 mol of ?ideal helium (He) gas. Part ?ca of this process is isothermal. (a) Find the pressure of the He at point ?a?. (b) Find the temperature of the He at points ?a?, ?b?, and ?c?. (c) How much heat entered or left the He during segments ?ab?, ?bc?, and ?ca?? In each segment, did the heat enter or leave? (d) By how much did the internal energy of the He change from ?a to ?b?, from ?b to ?c?, and from ?c to a?? Indicate whether this energy increased or decreased.

Solution 48P Introduction From the given pressure and volume at point c, we have to calculate the pressure at point a. Now knowing the pressure temperature and volume at each point, we can calculate the temperature at each point. Now knowing the molar specific heat of He, we can calculate the energy supplied to each segment. After that, by calculating the work done in each segment we can calculate the change in internal energy. Step 1 (a) The segment ca represents an isothermal process, hence we can write that Now from the figure we can see that P c 2.0 × 10 Pa 3 V c 0.040 m V = 0.010 m 3 a Hence the final pressure is 5 So the pressure at point a is 8.0 × 10 Pa.