A rigid container holds 3 of air. The air is stirred so that its pressure changes from 500kPa to 2000kPa, while its temperature is held at 50 ∘ C . The heat transferred is 200kJ. Assume the air to behave like an ideal gas with c v = 0.714 kJ kg ⋅ K . Find the final temperature, the change in internal energy, and the work done.

Question

A rigid container holds 3 of air. The air is stirred so that its pressure changes from 500kPa to 2000kPa, while its temperature is held at       50    ∘    C . The heat transferred is 200kJ. Assume the air to behave like an ideal gas with       c    v    =  0.714        kJ          kg      ⋅      K       . Find the final temperature, the change in internal energy, and the work done.

Royce Morrison · Accepted Answer

So, if I understood the problem correctly, you do work on the ideal gas by stirring it continuously at a constant volume. This increases the temperature of the gas and hence its pressure, as at a constant volume for a constant amount of gas,   P  ∝  T. You also transfer 200 kJ of heat.For the work done on the gas to increase the pressure at a constant volume, T cannot be constant, as P is a function of T. If T would have been constant, P would have been constant too.

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