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︰物理學系
考試日期（年月日）︰2019/10/15
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Thermal Physics Midterm Examination I
Date: October 15, 2019
1. At what temperature do the Fahrenheit and Kelvin scales give the same
reading? [20 points]
2. For an ideal gas, the slope of an isotherm is given by
(∂P/∂v)_T=-P/v,
and that of an isochore is
(∂P/∂T)_v=P/T.
Show that these relations give Pv=RT, the equation of state. [20 points]
3. A hypothetical substance has an expansivity β=2bT/v and an isothermal
compressibility κ=a/v, where a and b are constants. Show that the equation
of state is
v-bT^2+aP = constant. [20 points]
4. Ice at 0°C and at a pressure of 1 atmosphere has a density of 916.23
kg/m^3, while water under these conditions has a density of 999.84 kg/m^3.
How much work is done against the atmosphere when 10 kg of ice melts into
water? [20 points]
5. The pressure on 100 g of nickel is increased quasi-statically and
isothermally from zero pressure to 500 atm. Calculate the work done on the
material, assuming that the density and isothermal compressibility remain
constant at the values of 8.9×10^3 kg/m^3 and 6.75×^(-12) Pa^(-1),
respectively. [20 points]