Solution Found!
Figure P19.43 shows a p V -diagram for 0.0040 mol of ideal
Chapter 19, Problem 47P(choose chapter or problem)
Figure P19.43 shows a p ? V -diagram for 0.0040 mol of ?ideal H 2 gas. The temperature of the gas does not change during segment ?bc?. (a) What volume does this gas occupy at point c? (b) Find the temperature of the gas at points ?a?, ?b?, and ?c?. (c) How much heat went into or out of the gas during segments ?ab?, ?ca?, and ?bc?? Indicate whether the heat has gone into or out of the gas. (d) Find the change in the internal energy of this hydrogen during segments ?ab?, ?bc?, and ?ca?. Indicate whether the internal energy increased or decreased during each segment.
Questions & Answers
QUESTION:
Figure P19.43 shows a p ? V -diagram for 0.0040 mol of ?ideal H 2 gas. The temperature of the gas does not change during segment ?bc?. (a) What volume does this gas occupy at point c? (b) Find the temperature of the gas at points ?a?, ?b?, and ?c?. (c) How much heat went into or out of the gas during segments ?ab?, ?ca?, and ?bc?? Indicate whether the heat has gone into or out of the gas. (d) Find the change in the internal energy of this hydrogen during segments ?ab?, ?bc?, and ?ca?. Indicate whether the internal energy increased or decreased during each segment.
ANSWER:Solution 47P Introduction For the first part of the problem we have to first calculate the volume of the gas at point C. After knowing the volume we can calculate the temperature at each point, since the other parameter are known. Now knowing all this parameter and what kind of process it is (isothermal or isobaric or isochoric, etc) we can calculate the amount of energy supplied to it and work done by the gas. From this information we can calculate the change in internal energy in each process. Step 1 To calculate the volume at point c, let us consider the segment bc in the PV diagram. Since the process is isothermal we can write that PV = constant P 1 =1P V 2 2 Now in this segment, we have V = 0.20 L = 0.20 × 10 3m 3 1 P = 2.0 atm = 2.03 × 10 Pa 1 5 P 2 0.50 atm = 0.501 × 10 Pa Hence the final volume is So the volume of the gas at point c is 0.81 L.