Question

2) a) Find an expression for Cp in terms of Cy. Does this make sense? Explain. b) Calculate Co for a van der Waals gas in terms of V, T, and Cy. c) What are the dimensions of heat capacity? Does this make sense? Explain. d) At approximately the same latitude, a rain forest and a desert receive approximately equal free energy input from solar radiation per time. Why is the average temperature of a rain forest several degrees lower than a desert given identical energy input rates? Does this make sense in terms of your answer to part c?

Answer 1

a) According to the relation between Cp and Cv:

Cp - Cv = R

i.e. Cp = Cv + R

Yes, this makes sense because Cp is always greater than Cv.

b) Cp = Cv + R{1 + (2aP/R²T²)}

Here, P = RT/(V-b) - a/V²

c) The dimensions of heat capacity are J/K.

Yes, this makes sense because heat capacity is the amount of energy absorbed or released per certain temperature.