2. For N2(g), CP,m is nearly constant at 3.5R = 29.1 J/(mol K) for temperatures

Question

2. For N2(g), CP,m is nearly constant at 3.5R = 29.1 J/(mol K) for temperatures in the range 100 to 400 K and low or moderate pressures. (a) Calculate q, w, ?U, and ?H for the reversible adiabatic compression of 1.12 g of N2(g) from 400 torr and 1000 cm3 to a final volume of 250 cm3. Assume ideal gas behavior. (b) What would ?U and w be if the expansion connects the same initial and final states as in (a) but is done by having the perfect gas expand into a vacuum. I found q=0, w=deltaU= 40J, and delta H=2.00 J. I don't think these answers are reasonable. Please explain what equations i need to use.

Explanation / Answer

Total work is the sum of the work done at each process Total Work = Wac + Wcb + Wba W at ac = isobaric process = nR(delta)T W at cb = adiabatic process = -nCv(delta)T W at ba = isochoric process, therefore W= 0 Cp = 29.1 = 3.5R so Cv = 2.5R = 20.8 Total Work = (3)(8.31)(190) - (3)(20.8)(110) + 0 = 4,736.7 - 6,864 = -2,127.3

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