课程名称︰热物理 课程性质︰物理系大三必带 课程教师︰蔡政达 开课学院：理学院 开课系所︰物理系 考试日期（年月日）︰2020/01/07 考试时限（分钟）：110分钟 （如未明确表示，则不予发放） 试题 : 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] --

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