Consider the cyclic process 1 -> 2 -> 3 -> 4 -> 1 where we model the working flu
ID: 2120593 • Letter: C
Question
Consider the cyclic process 1 -> 2 -> 3 -> 4 -> 1 where we model the working fluid undergoing this cyclic process as n moles of an ideal gas whose specific heat at constant volume Cv is 7/2 R. The universal gas constant R = 8.31 J/ mole K given that:
1 -> 2 constant pressure expansions
2 -> 3 isothermal expansion
3 -> 4 constant volume cooling
4 -> 1 adiabatic compression
Complete the tables
State
Pressure (Pa)
Volume (m^3)
nR * Temperature (J)
1
.05
2500
2
.10
3
25,000
4
Process
U (J)
Q (J)
W (J)
1 -> 2
2 -> 3
3 -> 4
4 -> 1
Use the expression for the efficiency of this engine to be given by E = W/Qin and find the efficiency of this engine
State
Pressure (Pa)
Volume (m^3)
nR * Temperature (J)
1
.05
2500
2
.10
3
25,000
4
Explanation / Answer
1. P = 2500/0.05 = 50000 Pa
2. P = 50000 Pa , nR*T = 500000 J
3. V = 20 m^3 , nR*T = 500000 J
4. P = 22.57Pa , V = 20m^3 , nR*T = 451.33 J
1->2 U = -175000 J , Q = 225000 J , W = 50000 J
2->3 U = 0 J , Q = 264915.87 J , W = 264915.87 J
3->4 U = -173420.35 J , Q = -173420.35 J , W = 0
4->1 U = -38537.85 J , Q = 0 J , W = 38537.85 J