課程名稱︰熱物理
課程性質︰物理系大三必帶
課程教師︰蔡政達
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰2020/01/07
考試時限（分鐘）：110分鐘
（如未明確表示，則不予發放）
試題 :
Thermal Physics Final Examination
Date: January 7, 2020
1. Calculate the difference in the specific heat capacities c_p-c_v of copper
at 300K. Take β=4.9×10^(-5) K^(-1), κ=7.7×10^(-12) Pa^(-1), and v=
7.1×10^(-3)m^3 kilomole^(-1). [20 points]
2. The gibbs function of a certain gas is
CP^2 DP^3
G = nRT ln(P) + A + BP + ── + ──,
2 3
where A, B, C, and D are constants. Find the equation of state of the gas.
[20 points]
3. (a) A van der Waals gas undergoes an isothermal expansion from specific
volume v_1 to specific volume v_2. Calculate the change in the specific
Helmholtz function. [10 points]
(b) Calculate the change in the specific internal energy in terms of v_1
and v_2. [10 points]
4. Show that for a closed system consisting of two phases coexisting in equil-
ibrium at a temperature T and under a pressure P,
∂P T dP 2
(──) = - ─ (──). [20 points]
∂V s C_v dT
Here dP/dT is the slope of the phase equilibrium curve.
5. Consider a solid whose equation of state is
PV + f(V) = AU,
where f(V) is a function of the volume only and A is a constant. Show that
C_v→0 as T→0. [20 points]