A heat engine is composed of of a monatomic ideal gas which runs in the followin

Question

A heat engine is composed of of a monatomic ideal gas which runs in the following cycle: At point A the pressure is 3 atm, the volume is 2.1 liters and the temperature is 300 K. During the transition A to B the pressure is constant and the volume doubles to 4.2 liters. From B to C the pressure decreases at constant volume to 1.5 atm. From C to A there is a compression at constant temperature until the pressure is again 3 atm, where again the volume is 2.1 liters and the temperature is 300 K. A) What is the temperature at point B? B) What is the work done BY the gas in the transition A to B? (Signs are important!) C) What is the heat input into the gas for the transition A to B? (Signs are important!) D) What is the work done in the transition B to C? (Signs are important!) E) What is the heat input into the gas for the transition B to C? (Signs are important!) F) For the constant temperature transition C to A, 436.68272 J of heat are taken out of the gas. What is the work done ON the gas in the transition? G) What is the efficiency of this heat engine? H) What is the efficiency of a Carnot cycle running between the lowest and highest temperature of the cycle above?

Explanation / Answer

as we know PV = nRT as in A and B, P is constant comparing P = nRT/V on both sides P , n , R are constant for both phases Ta/Va = Tb/Vb Tb = Ta*Vb/Va = 300*4.2/2.1 Tb = 600 K in case of B & C Pb/Tb = Pc/Tc Tc = Pc*Tb/Pb = 1.5 * 600 / 3 = 300 K effeciency durin running from lowest to high temperatures nth = (1 - Tb/Tc)*100 = (1 - 300/600)*100 = (1 - 1/2)*100 = 1/2*100 = 50 %

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