Answer to Question #1597 in Molecular Physics | Thermodynamics for Zubair Ulhuq

Question

One kilogram of air in a piston-cylinder assembly undergoes two processes in series from an initial state where P1=0.5MPa, T1=227C.
Process 1-2: Constant temperature expansion until the volume is twice the initial volume.
Process 2-3: Constant-volume heating until the pressure is again 0.5MPa

a) Sketch the two processes in series on a clearly labeled P-v diagram.
b) Assuming ideal gas behaviour, determine:
(i) The pressure at state 2, in MPa
(ii) The temperature at state 3, in C
(iii) For each of the two processes the work and heat transfer, each in kj

Answer 1

1-2 - isothermal process, P1V1 = P2V2, if V2=2V1, P2 = P1/2 = 0.5 MPa/2 = 0.25MPa.

W = m/M RT ln(V2/V1) = 1000[g]/29 [g/mol] *8.31 [J/(mol K)] (227+273)[K] ln2 = 99311 J = 99.3 kJ

2-3 - isochoric process, P2/T1 = P1/T3, therefore T3 = P1T1/P2 = 2T1 = 500*2 = 1000 [K] = 727 C; W=0.