Unit 2 Homework 2: Laws of Thermodynamics, Maxwell’s equations

(Monday Feb 21 by 5pm)

1.  (a) This problem will illustrate that work is a path function and not a state function. Consider an ideal gas that occupies 2.25 L at 1.33 bar. Calculate the work required to compress the gas isothermally to a volume of 1.50 L at a constant pressure of 2.00 bar followed by another isothermal compression to 0.800 L at a constant pressure of 2.50 bar. Compare the result with the work of compressing the gas isothermally and reversibly from 2.25 L to 0.800 L. What is the change in energy, DE, for these two processes? (b) One mole of an ideal gas initially at a pressure of 2.00 bar and a temperature of 273 K is taken to a final pressure of 4.00 bar by the reversible path defined by P/V = constant. Calculate the values of ΔE, ΔH, q, and w for this process. Take to be equal to 12.5 J mol-1 K-1.

2.  Use the following data to calculate the value of DvapHo of water at 298 K.

DvapHo at 373 K is 40.7 kJmol-1

(l) = 75.2 Jmol-1K-1

(g) = 33.6 Jmol-1K-1

3. Use the following data to calculate the standard reaction enthalpy of the water-gas reaction (C (s) + H2O (g) ® CO (g) + H2 (g)) at 1273 K. Assume that the gases behave ideally under these conditions.

4. The internal energy depends on volume. Derive this dependency by considering the Helmholtz thermodynamic state function. Generate the plot shown on page 891 using Excel. This shows how the molar internal energy of ethane changes with pressure. In deriving the plot, assume ethane behaves like a van der Waals gas. Derive explicit relationships for (¶U/¶V)T for (a) an ideal gas, (b) a van der Waals gas, (c) a Redlich-Kwong gas, and (d) a gas obeying the virial equation of state (up to the second virial coefficient).

5. Repeat the last question, but now determine how enthalpy varies with pressure. Derive (¶H/¶P)T. Generate the plot shown on page 896 using Excel. This shows how the molar enthalpy of ethane changes with pressure. In deriving the plot, assume ethane behaves like a van der Waals gas. Derive relationships for (¶H/¶P)T for (a) an ideal gas, (b) a gas obeying the virial equation of state (up to the third virial coefficient), and (c) a gas obeying the equation of state .

6. By using the Maxwell relation to determine how entropy varies with pressure, we derived the expression for the entropy of the hypothetical ideal gas at 1 bar: . This equation represents the entropy of the standard state and is used to obtain the nonideality correction to the entropy. Experimentally determined entropies are commonly adjusted for nonideality by using an equation of state called the modified Berthelot equation:

Show that this equation leads to the correction

This result needs only the critical data for the substance. Use this equation along with the critical data in Table 16.5 to calculate the nonideality correction for N2(g) at 298.15 K. Compare your result with the value used in Table 21.1.