課程名稱︰普通物理學甲上
課程性質︰必修
課程教師︰林敏聰老師
開課系所︰電機系
考試時間︰無限
試題 :Total: 150%
1. Please write down the three laws of thermodynamics with brief interpretation. (15%)
2. Please prove the relation, pV^γ= a constant, during an adiabatic process of an ideal gas, where γ= Cp / Cv（p, v 下標）, the ratio of the molar specific heats for the gas. (10%)
3. (a) Please derive the entropy change: ΔS = S_f – S_i
= n R ln( V_f / V_i ) + n Cv ln( T_f / T_i ) for all reversible process that take the gas from state i to state f. (10%)
(b) Please use this relation to calculate the change in the entropy for a free expansion process from V to 2V. Please also give the reason that you may do in this way. (10%)
(c) Derive this increase of entropy with statistical mechanics (using the Boltzmann's entropy equation S = k ln W, where k is the Boltzmann's constant, W the multiplicity of the configuration). (10%)
(You can use the Stirling's Approximation: ln N! = N ln N - N .)
4. Please express (in string tension τ and mass length density μ) and derive the equation for the wave speed v on stretched string from Newton's second law. (10%) )
5. An apparatus that liquifies helium is in a room maintained at 300K. If the helium in the apparatus is at 4.0K, what is the minimum ratio of the heat delivered to the room to heat removed from the helium? (10%)
6. One mole of an ideal gas are expanded from V_1 to V_2 = 3 V_1. If the expansion is isothermal at temperature 300K, find (a) the work done by the expanding gas and (b) the change in its entropy. (c) If the expansion is reversibly adiabatic instead of isothermal, what is the change of entropy of the gas? (15%)
7. What is the entropy change (a) for any reversible CLOSED cycle and (b) for the irreversible process whose final T and V are the same as the initial ones. (20%)
8. Please give a clear argument by using the concept of entropy to explain that the heat will always flow from the high temperature to the low temperature objects if there is no external work. (10%)
9. In an experiment, 200g of Al (with a specific heat of 900 J/kg．K）at 373K is mixed with 50.0g of water at 293K with the mixture thermally isolated. (a) What is the equilibrium temperature? What are the entropy changes of (b) the Al, (c) the water, and (d) the Al-water system? (20%)
10. For adiabatic processes in an ideal gas, show that (a) the bulk modulus is given by
dp
B = -V ── = γp,
dV
And therefore (b) the speed of the sound in the gas is
γp γRT
v = sqrt( ── ) = sqrt( ─── )
ρ M (20%)
11. Good luck!!! Happy NEW YEAR!
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.7.59