Question

Start with an ideal gas of volume 4m^3, at a pressure of 1200Pa, and temperature 289K. Construct a cycle using 3 or more processes (of your choice). For each process in your cycle calculate the Q, ?U, and W. Calculate the net change in each of these quantities for the entire cycle, and determine whether the work as a result of the cycle is done ON or BY the system.

Answer 1

Let the 3 cycle process be;
Process 1-2: Isothermal compression to V2 = 1m3
Process 2-3: Isobaric expansion to V3 = 2 m3
Process 3-1: Adiabatic expansion
Using pV = nRT we have, number of moles, n = 1200*4/(8.314*289) = 2 moles
For isothermal process 1-2, T2 = T1 = 289 K and pV = constant.
Hence, 1200*4 = p2*1. So p2 = 4800 Pa.
For isobaric process 2-3, p2 = p3 = 4800 Pa and V/T = constant.
Hence, 1/289 = 2/T3. So T3 = 578 K
For isothermal process 1-2:
Work done, W1-2 = nRT ln(V2/V1) = 2*R*289 ln(1/4) = -801.3*R
Internal energy change, ?U1-2 = 0. (Since isothermal process).
Heat transfer Q1-2 = W1-2 + ?U1-2 = -801.3*R
For isobaric process 2-3:
Work done, W2-3 = p (V3-V2) = 4800*(2-1) = 9600 J
Internal energy change, ?U2-3 = nCv(T3-T2) = 2*Cv*(578-289) = 578 Cv
Heat transfer Q2-3 = W2-3 + ?U2-3 = 9600 + 578*Cv
For adibatic process 3-1:
Work done, W3-1 = (p1V1-p3V3)/(1-?) = (1200*4-4800*2)/(1-?) = 4800/(?-1)
Heat transfer Q3-1 = 0 (since adiabatic process)
Internal energy change, ?U3-1 = Q3-1 - W3-1 = -4800/(?-1)