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）︰2019/12/03
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 II
Date: December 3, 2019
1. The equation of state for radiant energy in equlibrium with the temperature
of walls of a cavity of volume V is P=aT^4/3, where a is a constant. The
energy equation is U=aT^4V.
(a) Show that the heat supplied in an isothermal doubling of the volume of
the cavity is (4/3)aT^4V. [10 points]
(b) Show that in an adiabatic process, VT^3 is constant. [10 points]
2. Show that
(a) ∂h βμ
(──) = c_p(1- ──). [7 points]
∂T v κ
(b) ∂h μc_p
(──) = ──. [7 points]
∂v T vκ
(c) ∂T μ
(──) = ──────. [6 points]
∂v h v(λβ-κ)
3. A Carnot engine is operated between two heat reservoirs at temperatures of
400K to 300K.
(a) If the engine recieves 1200 kilocalories from the reservoir at 400K in
each cycle, how much heat does it reject to the reservoir at 300K? [5
points]
(b) If the engine is operated as a refrigerator (i.e., in reverse) and
recieves 1200 kilocalories from the reservoir at 300K, how much heat
does it deliver to the reservoir at 400K? [5 points]
(c) How much work is done by the engine in each case? [5 points]
(d) What is the efficiency of the engine in (a) and the coefficient of
performance in (b)? [5 points]
(More Problems on the Reverse Side!)
4. An ideal monatomic gas undergoes a reversible expansion from specific from
specific volume v_1 to specific volume v_2.
(a) Calculate the change in specific entropy Δs if the expansion is
isobaric. [7 points]
(b) Calculate Δs if the process is isothermal. [7 points]
(c) Which is larger? By how much? [6 points]
5. (a) Show that for reversible changes in temperature at constant volume,
∂s
c_v = T(──) . [10 points]
∂T v
(b) Assume that c_v = aT+bT^3 for a metal at low temperatures. Calculate
the variation of the specific entropy with temperature. [10 points]