A balloon initially contains air at 25oC and 450 kPa, with a volume of 0.10 m3. The air inside the balloon is heated and the balloon expands until the volume is 0.25 m3. The pressure and volume follow the relationship PV1.3 = constant during the process. Determine the final temperature of the air, and the amount of heat added.
Given: Air; T1 = 25oC = 298 K; P1 = 450 kPa; V1 = 0.10 m3; V2 = 0.25 m3; PV1.3 = 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 with n = 1.3:
P2 = P1V11.3 / V21.3 = 136.7 kPa
W = 36.05 kJ
m = P1V1/RT1 = 0.526 kg
T2 = P2V2/mR = 226.3 K
Q = m cv (T2 – T1) + W = 8.98 kJ
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