PHY 3513: Spring 2006
Final Exam
Name:_________________________
1. Consider the Joule cycle heat engine consisting of two isobars (at pressures P1 and
P2)and two adiabats. Assuming that the working substance is an ideal gas with
the constant specific heat capacities, Cp and Cv = Cp/γ, show that the efficiency of
this engine can be written as
⎛ 1⎞
⎜ 1− ⎟⎟
γ⎠
⎛ P ⎞ ⎜⎝
η = 1 − ⎜⎜ 1 ⎟⎟
⎝ P2 ⎠
2. Suppose that the volume thermal expansivity β = (v-a)/vT and κ = 3(v-a)/(4Pv).
Show that the equation of state is given by
P3/4(v-a) = AT
Where a and A are constants.
3.
(a) If Cv = a(P)T + b(P)T3 at low temperatures (as is the case with most
metals, ask Stewart or Andraka), calculate the temperature variation of the
entropy.
(b) Calculate the temperature dependence of the coefficient of volume thermal
expansion (vβ = dv/dT|P) from the entropy in part (b). If β>o, what does
that say about the coefficients a(P) and b (P).