課程名稱︰材料熱力學一
課程性質︰必修
課程教師︰林招松
開課學院：工學院
開課系所︰材料系
考試日期（年月日）︰101.10.17
考試時限（分鐘）：180 分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Gas constant R = 8.3144 J/(mole K) = 1.987 cal/(mole K)
= 0.082057 (liter-atm)/(mole K)
1. One mole of the ideal gas at P1 atm and T1 K is adiabatically expanded to
P2 atm and T2 K. (15%)
(1) Prove the work (W) performed during this process is
cvY1[1-(P2/P1)^((γ-1)/γ)] if the expansion is performed reversibly. Where
cv is the constant volume heat capacity and γ=cp/cv
(2) Prove mathematically or schematically the W performed is the maximum work.
2. One mole of a monoatomic ideal gas (cv=3R/2) is subjected to the following
sequence of steps
a. Starting at 250 K and 5 atm, the gas expands freely into a vacuum to triple
its volume.
b. The gas is next heated reversibly to 400 K at constant volume.
c. The gas is reversibly expanded at constant temperature until its volume
is again tripled.
d. The gas is finally reversibly cooled to 250 K at constant pressure.
Calculate the values of q and w and the change in U, H, and S during each
step and the whole sequence. (20%)
3. Draw on the temperature-entropy coordinated the Carnot cycle and based on
this diagram, prove the efficiency of the Carnot cycle is equal to 1-(T1/T2),
where T1 and T2 are the temperature of the reservoirs at high and low
temperature, respectively. Hint: plot the Carnot cycle on the coordinate with
temperature as the abscissa and entropy as the ordinate. (15%)
4.
(1) Prove that cp-cv = (δV/δT)(←定P)*[P+(δU/δV)(←定T)] (7%)
(2) What the (δU/δV)(←定T)*(δV/δT)(←定P) term stands for ?
Why (δU/δV)(←定T)*(δV/δT)(←定P) is significant for solids but can be
neglected for ideal gases ? (8%)
5. Answer the following question (35%)
(1) Is the infinitesimal quantity dF = (x^2-y)dx + xdy an exact differential ?
(2) Is thermodynamics first law sufficient to deal with the equilibrium of a
single component system ? Why ?
(3) For the evaporation of one mole of water in a thermo-stalled piston and
cylinder containing water and water vapor, would you expect the amount of
heat exchanged with the heat bath during reversible evaporation to be greater
than, the same as, or less than the amount of heat exchanged with the heat
bath during irreversible evaporation ? Why ?
(4) Do you agree the statement: The sum of the entropy change of the system
and of the surrounding is always zero. Why ?
(5) Name and describe briefly three irreversible processes during which the
entropy of the system increases.
(6) What is the sponsaneity of an irreversible process ?
(7) Show that for an ideal gas δq is not an exact differential but δq/T is.
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.243.14