Air occupies a balloon that has an initial volume of 0.05 m3. Initially, the air has a temperature of 20oC and a pressure of 125 kPa. The air is heated, and the balloon expands until the volume of 0.25 m3. The pressure and volume are related through pVn = constant. Develop a computer program model for analyzing such a process/device. Plot the final temperature of the air, the work done, and the heat transfer for values of n = 1.1, 1.2, 1.3, 1.4, and 1.5.
Given: Air; T1 = 20oC = 293 K; P1 = 1000 kPa; V1 = 0.05 m3; V2 = 0.25 m3; PVn = constant
Assume: ?KE = ?PE = 0. The air is an ideal gas with constant specific heats (cv = 0.718 kJ/kg-K; R = 0.287 kJ/kg-K)
What will be an ideal response?
Solution: This is a closed system, and the First Law will reduce to
Q – W = m (u2 – u1)
The work is moving boundary work, with the process being polytropic:
P2 = P1V1n / V2n = 1000 (0.2)n
m = P1V1/RT1 = 0.595 kg
T2 = P2V2/mR
Q = m cv (T2 – T1) + W
For the different values of n:
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