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

Question

heat engine is composed of of a monatomic ideal gas which runs in the following cycle: At point A the pressure is 2.7 atm, the volume is 2.3 liters and the temperature is 300 K. During the transition A to B the pressure is constant and the volume doubles to 4.6 liters. From B to C the pressure decreases at constant volume to 1.35 atm. From C to A there is a compression at constant temperature until the pressure is again 2.7 atm, where again the volume is 2.3 liters and the temperature is 300 K.

Part E What is the heat input into the gas for the transition B to C? (Signs are important!)

Part F For the constant temperature transition C to A, 430.4444 J of heat are taken out of the gas. What is the work done ON the gas in the transition?

Part G What is the efficiency of this heat engine?

Part H What is the efficiency of a Carnot cycle running between the lowest and highest temperature of the cycle above?

Explanation / Answer

A --> B   pressure is constant

Pa = 2.7 atm

Va = 2.3L

Ta = 300K

Vb = 2Va = 4.6 L

Pb = Pa = 2.7 atm

Tb = ?

B-->c

Pc = 1.35 atm

vc = vb = 4.6 L

Tc = ?

C -->A isothermal

Tc = Ta = 300 K

E)

QBc = -dU

dU = n*R*dT/(gamma-1) = (Pb-pc)*V/(gamma-1)

dU = (2.7-1.35)*10^5*4.6*10^-3/(1.67-1)

dU = 926.8 J

dQ = -926.8 J

F)

W = -Q = -430.4444 J

G)

n = 1

H)

from A to B

Tb/Ta = Vb/Va

Tb/300 = 2

Tb = 600 K

efficiency = 1- Ta/Tb = 1-300/600 = 1-1/2 = 50%

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