In the figure above, a closed thermodynamic cycle, known as the Stirling Cycle,
ID: 1487599 • Letter: I
Question
In the figure above, a closed thermodynamic cycle, known as the Stirling Cycle, is shown. It consists of four processes using a diatomic ideal gas: a) The gas expands at a constant temperature, TH=400 K, from V1 to V2, b) The gas is cooled at constant volume, V2, from THto TC=270 K, c) The gas is compressed at constant temperature, TC, from volume V2 to V1, d) The gas is heated at constant volume, V1, back to the initial state.
Assume that V2 = 4.5 V1 and there are 0.8 moles of gas.
What is the total heat exchanged with the environment, Q, for one entire cycle of the engine? (Your answer should be in Joules but don't include the units in your answer.)
Explanation / Answer
1--> 2 isothermal process
W1->2 = 2.303*n*R*T*log(v2/v1)
W1-->2 = 2.303*0.8*8.314*log(4.5) = 10 J
W2-->3 = P2*(V1-v2) = P2*(v2/4.5 - v2) = P2*v2*(1/4.5-1)
W2--3 = n*R*T*(1/4.5-1)
W2--3 = 0.8*8.314*400*((1/4.5)-1) = -2069.3 J
W3--1 = p*dV = 0
Wtot = 10-2069.3 = -2059.3 J
in closed process dU = 0
dQ = dU + dW
dQ = -2059.3