An engine using 1 mol of an ideal gas initially at 22.3 L and 454 K...
An engine using 1 mol of an ideal gas initially at 22.3 L and 454 K performs a cycle consisting of four steps: 1) an isothermal expansion at 454 K from 22.3 L to 40 L ; 2) cooling at constant volume to 270 K ; 3) an isothermal compression to its original volume of 22.3 L; and 4) heating at constant volume to its original temperature of 454 K . Find its efficiency. Assume that the heat capacity is 21 J/K and the universal gas constant is 0.08206 L · atm/mol/K = 8.314 J/mol/K. Answer in units of %.
Homework Answers
Ans: Given n = 1 mol, V1 = 22.3 L, T1 = 454 K => P1 = nRT1/V1 = 1.671 atm
Step-1: 
T = 0 =>
U = 0, T2 = 454 K, V2 = 40L =>
P2 = nRT2/V2 = 0.931 atm
Work done by gas
From 1st law of thermodynamics,
Step-2:
V = 0 =>V3 = 40L,
W = 0, T3 = 270 K =>
T = 270 - 454 = -184 K
W2 = 0 J
Q2 =
U = nCT
= 1 x 21 x -184 = -3864 J
Step-3: T
= 0 =>
U = 0, T4 = 270 K, V4 = 22.3L =>
P4 = nRT4/V4 = 0.994 atm
Work done by gas
From 1st law of thermodynamics,
Step-4:
V = 0 =>
W = 0 =>
T = 454-270 = 184 K
W2 = 0 J
Q4 =
U = nCT
= 1 x 21 x 184 = 3864 J
Total Heat given to the system is Q = Q1 +Q4 = 6069.446 J
Net work done W = W1+ W2+ W3+ W4 = 893.837 J
Efficiency 
= W/Q = 0.1473 = 14.73%
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