2002.1.13. total:150
1.Please write down the three laws of thermodynamics with brief
interpretation.
(15%)
r
2.Please prove the relation,pV (r為gama打不出來,且r上標,V之r次方)=a constant,
during an adiabatic process of an ideal gas,where r=Cp/Cv(p,v下標),the
ratio of the molar specific heats for the gas.
(5%)
3.A solid cylinder is attached to a horizontal massless spring so that it can
roll without slipping along a horizontal surface. The spring constant k is
3.0 N/m. If the system is released from rest at a position in which the
spring is stretched by 0.25m,(原卷有附圖)find
(a)the translational kinetic energy and
(b)the rotational kinetic energy of the cylinder as it passes through the
equilibrium position.
(c)Show that inder these conditions the center of mass of the cylinder
executes simple harmonic motion. What is its period?
(15%)
4.(a)Please derive the entropy change:DS=S-S=nRln(Vf/Vi)+nCvln(Tf/Ti) (D為
delta的大寫,打不出來;f,i,v均為下標) for all reversible processes that
take the gas from state i to state f.
(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.
(c)Derive this increase of entropy with statistical mechanics (using the
Boltsmann's entropy equation S=klnW,where k id the Boltzmann's const
,W the multiplicity of the configuration).
(You can use the Stirling's Approximation:lnN!=NlnN-N.)
(each10%)
5.Please express (in string tension T(tou打不出來) and mass length density
u(miew打不出來)) and derive the equation for the wave speed v on stretched
string from Newton's second law.
(10%)
6.An apparatus that liquefies 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?
(15%)
7.Please construct the plots of P versus V,T versus S,and S versus Einternal
(internal下標)for the isothermal expansion and isobaric expansion
thermodynamic process.
(15%)
8.One mole of an ideal gas are expanded from V1 to V2 =3V1 (1,2下標). 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%)
9.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 the
initial ones.
(20%)
10.Consider a damped simple harmonic motion with the total force EF=-kx-bv
(E表Sigma打不出來),where k is force constant of the spring,x the
displacement,v the velocity,b the damping constant. Please write down and
solve the (differential) equation of motion from the Newton's Second Law.
(10%)
11.Good luck!!!and Happy NEW YEAR!
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