CALC A heat engine operates using the cycle shown in ?Fig. P20.41?. The working substance is 2.00 mol of helium gas, which reaches a maximum temperature of 327o C. Assume the helium can be treated as an ideal gas. Process ?bc is isothermal. The pressure in states a and c is 1.00 X 105 Pa, and the pressure in state b is 3.00 X 105 Pa. (a) How much heat enters the gas and how much leaves the gas each cycle? (b) How much work does the engine do each cycle, and what is its efficiency? (c) Compare this engine’s efficiency with the maximum possible efficiency attainable with the hot and cold reservoirs used by this cycle.
Solution 43P Introduction From the given cycle, we will calculate the heat supplied to the system and total heat released by the system. The remaining heat will be converted to work done by the system. From the work done by the system and the total energy supplied to the system, we can calculate the efficiency of the engine. Also by knowing the high and low temperature of the system we can calculate the efficiency of the carnot cycle and then we can compare the two efficiency. Step 1 From the given diagram, we can see the whole cycle is consist of three process. a b, b c, and c a . The process a b is an isochoric process, b c is an isothermal process and c a is an isobaric process. As b c is an isothermal process the temperature at b and c will be same. Also, in a b is an isochoric process and pressure increases in this process, hence the temperature at b is maximum. So we know that 5 P a 1.00 × 10 Pa 5 P b 3.00 × 10 Pa P = P = 1.00 × 10 Pa5 c a T b T =c327°C = 600 K So we have