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CALC You build a heat engine that takes 1.00 mol of an
Chapter 20, Problem 41P(choose chapter or problem)
CALC You build a heat engine that takes 1.00 mol of an ideal diatomic gas through the cycle shown in ?Fig. P20.39?. (a) Show that process ?ab is an isothermal compression. (b) During which process(es) of the cycle is heat absorbed by the gas? During which process(es) is heat rejected? How do you know? Calculate (c) the temperature at points ?a?, ?b?, and ?c?; (d) the net heat exchanged with the surroundings and net work done by the engine in one cycle; (e) the thermal efficiency of the engine.
Questions & Answers
QUESTION:
CALC You build a heat engine that takes 1.00 mol of an ideal diatomic gas through the cycle shown in ?Fig. P20.39?. (a) Show that process ?ab is an isothermal compression. (b) During which process(es) of the cycle is heat absorbed by the gas? During which process(es) is heat rejected? How do you know? Calculate (c) the temperature at points ?a?, ?b?, and ?c?; (d) the net heat exchanged with the surroundings and net work done by the engine in one cycle; (e) the thermal efficiency of the engine.
ANSWER:Solution 41P Step 1: We need to show process a-b is isothermal compression Data given P a 2 × 10 Pa5 P = 4 × 10 Pa5 b 3 V a 0.010 m V b 0.005 m 3 P = 0.010 m 3 c 5 V c 4 × 10 Pa From ideal gas equation we have PV = nRT nR = constant Consider P V = T a a a 5 3 3 2 × 10 Pa × 0.010 m = 2 × 10 K Similarly P V = T b b b 5 3 3 4 × 10 Pa × 0.005 m = 2 × 10 K From the above calculations we have T a T b This shows the reaction from a to b is isothermal compression