Study problems, Chapter 3

1. Derive the thermodynamic equation of state

and evaluate it for a perfect gas.

2. (a) For 1 mol of an ideal gas, show that

(b) Show that dV is an exact differential.

(c) Using the result from (a), we may write the following expression for reversible expansion work:

Show that dw is not an exact differential.

3. Use the ideal gas law to obtain the three functions p = g(T,V), V = h(T,p), and

T = f(p,V). Show that the cyclic rule, is obeyed.

4. Because U is a state function, . Using this

result,show that for a perfect gas.

5. The expansion coefficient, a, of a substance is given by ,and the isothermal compressibility, k, is given by Evaluate a and k for an ideal gas.

6. Show that the differential is exact.

7. For a constant amount of gas the pressure is a function of temperature and volume,

p = p(T,V). Write the expression for dp, and use the ideal gas law to show that p is a state function.