黃良平91下期中
2003. 4.29
1.A particular gas is enclosed in a cylinder with a moveable piston. It is
  observed thatr if the walls are adiabatic, a quasi-static increase in volume
  results ina decrease in pressure according to the equation:
  (P^2)(V^5)=constant (Q=0)
  Find the quasi-static work done on the system, if the system evolves along
  the adiabat. Initially Pi=10^5 Pa, Vi=9 dm^3. In the final state
  Pf=3*10^5 Pa.

2.Consider a system whose Energy(U) is given by the function U=4S^2 + 3V
  i.e. a function U(S,V)
  Obtain an expression for A(T,V), the Helmholtz free energy.

3.Assuming that dry air contains 79% N2 and 21% O2 by volume, calculate the
  density(in grams/liter) of moist air at 25度C and 1atm pressure when the
  relative humidity is 60%. The vapor pressure of water at 25度C is 23.76mmHg.

4.For a gas which obeys the equation of state V(bar)=RT/P + b + cP
  show that the activity coefficient γ(bar)=exp(2bP + c(P^2))/2RT

5.a.Show clearly that (δU/δV)T = T(δP/δT)V - P
  b.Show that (δU/δV)T = 0 for an ideal gas
  c.Evaluate (δU/δV)T (in J/L) for one mole of Xe at 298K and 1atm assuming
    it follows the eqiation of state (V-nb)P = nRT where b has the value
    0.051L/mol and is a constant.

6.For a gas following V(bar) = RT/P + (b - a/RT)
  What is the inversion temperature for the Joule-Thomson effect? What is the
  sign of ΔT below the inversion temperature?

7.According to Debye equation the heat capacity of a solid is proportional to
  the temperature cubed at low temperatures: Cp(T) = const*T^3
  Show that the entropy at a temperature T' is given by S(T') = Cp(T')/3
  When the Debye equation holds.

8.Derive the expression for (δH(bar)/δP)T for a gas following the virial
  equation P*V(bar) = RT + B(T)P