Exam 1     20 September 1999
Solutions

Answer any 4 questions!
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  1. The atmosphere on Jupiter is only 160 K at the cloud tops. Its composition is roughly 92.5% H2, 7.2% He, 0.15% CH4, and 0.15% NH3 in mole percent. (There's many more molecules at ignorable concentrations like the H2S that makes the yellows in Jupiter's bands.)

    At a depth in Jupiter's atmosphere where the pressure is 1 bar, what is the mean free path for the molecules given that s = 0.266 nm2 is the composition-weighted average cross-section for H2 and He?

  2. Derive the expression for DT for adiabatic expansion (or compression, it's the same expression) processes in terms of Ti and both Vi and Vf (where, of course, i means initial and f means final).

  3. You pump up a bicycle tire by compressing (adiabatically) air at 1 bar and 25°C into a volume of 1.3×10-3 m3 at 5 bar. If the air is ideal, and its CP = 29.17 J mol-1 K-1, what will the temperature of the air inside the tire become? Now you know why hand pumps get so bloody hot. (Ignore the temperature dependence of CP.)

    Use a P,T form of the adiabatic expression or you'll drive yourself crazy.

  4. Find the general total differential dT given that T is a function of p and V. Express the answer in terms of the expansion coefficient, a, and the isothermal compressibility, kT. Then substitute the ideal gas expressions for a and kT, and verify by direct integration that the partials yield Charles' laws for T,V and T,P. (That way you know you got it right.)

  5. How many liters of methane at STP does it take to boil a liter of water? The water starts at 25°C and has CP = 75.29 J mol-1 K-1 and a DvapH = 40.66 kJ/mol. Ignore temperature variations in these parameters (and those below).

    Molecule CH4(g) O2(g) CO2(g) H2O(liq)
    DfHq, kJ/mol - 74.81 0.00 - 393.51 - 285.83

  6. Benzene is a rotten ideal gas. Its van der Waals parameters are a = 18.24 atm L2/mol and b = 0.1154 L/mol. Find its compression factor, Z, at 100°C. (It only boils at 80°C!)
Last modified 19 September 1999