Question

4. You are asked to perform thermodynamic analysis for a real gas that obeys the following equation of state: aP where "a" and "b" are constants (the numerical value of these constants is not important for this problem). You also know that the real gas has the following molar heat capacity, which you can assume depends only on the temperature: Cpm = A + BT with T in kelvin. Also, 2aPaP2 Note that, since the gas is real, the relationship between cp.m and cvm is more complicated than for an ideal gas Again, the numerical values of the constants "A" and "B" are not important. Note that you might not need to use all information given to solve this problem. a) (30 points) Consider a constant pressure reversible process where the gas expands, as a closed system, from an initial temperature T1 to a final temperature T2. The pressure is constant at a value of "Po". 1. Calculate the heat (on a molar basis) transferred in this process. 2. Determine the molar internal energy change for this process. Express your answers as equations in terms of only T1, T2, A, B, C, a, b, R, and Po. 3. What would the molar internal energy change be for an ideal gas with the same constant pressure molar heat capacity? b) (5 points extra credit). Consider a reversible constant temperature process where the real gas expands from a pressure of P1 to a final pressure of P2 at a constant temperature To". Calculate the molar work in this process. Express your answer in terms of R, P1, P2, a, b, and To.

Answer 1