90年林敏聪 大一普通物理学 考古题 total 150 points 1. Please write down the three laws of thermodynamics with brief interpretation. (15%) 请写出热力学三大定律并作简单的解释。 r 2. Please prove the relation, pV = a(常数) constant,during an adiabatic process of an ideal gas,where r=Cp/Cv(p,v下标),the ratio of the molar specific heats for the gas. (5%) r 请证明此关系式 pV =a(常数)，在一个理想气体的绝热过程，r=Cp/Cv(p,v下标)，是气体莫耳比热的比率。 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,(原卷有附图)find (a)the translational kinetic energy (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%) 一个实心均匀的圆柱体系在一个水平没什麽质量的弹簧上,如此以至於它(圆柱体)可以滚而不会沿着水平面滑动。又这个弹黄的k (弹性系数)是 3N/m。 这个系统由静止释放，而绳子的原长是0.25m，则: (a) 平移动能? (b) 当圆柱体通过平衡位置时，圆柱体的转动动能是多少? (c) 当这个圆柱体的质心在做简谐运动时，它的周期为何? 4. (a)Please derive the entropy change:DS=S-S=nRln(Vf/Vi)+nCvln(Tf/Ti) (D为 delta的大写,打不出来;f,i,v均为下标) for all reversible processes that take the gas from state i to state f. 请推论”熵”变化: DS=S-S=nRln(Vf/Vi)+nCvln(Tf/Ti) (D为delta的大写,打不出来;f,i,v均为下标)对所有可逆反应过程，且气体由状态i变成状态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. 请用上面的关系求体积V 到 2V ，此这个自由膨胀过程计算”熵”的变化。 也请说明你为什麽要透过这个方法求的原因。 (c)Derive this increase of entropy with statistical mechanics (using the Boltsmann's entropy equation S=klnW,where k is the Boltzmann's const ,W the multiplicity of the configuration). (You can use the Stirling's Approximation:lnN!=NlnN-N.) 用统计力学推论”熵”的增加 (使用 Boltsmann's 的”熵等式”: S=klnW，k是Boltzmann常数，W架构的多样性) (你可以使用:the Stirling's Approximation:lnN!=NlnN-N.) (each10%) 5. Please express (in string tension T(tou打不出来) and mass length density u(miew打不出来)) and derive the equation for the wave speed v on stretched string from Newton's second law. 请表达(在绳子张力 T 和线密度u中和从牛顿的第二定律得到伸开的绳子上波速V的等式)。 (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%) 一个装置保持在300K的低温环境之下保持氦(He)的液化。如果氦(He)所处的环境变成了4.0K,把氦(He)由300K的环境移到4.0K的环境的热的最小比率是多少? 7. Please construct the plots of P versus V,T versus S,and S versus Einternal (internal下标)for the isothermal expansion and isobaric expansion thermodynamic process. (15%) 请建构一个恒温膨胀和等压膨胀热力学过程之中:P相对於V的图表,T相对於S ,和S相对於Einternal(下标)。 8.One mole of an ideal gas are expanded from V1 to V2 =3V1 (1,2下标). 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%) 一个1mole的理想气体从V1膨胀到V2 =3V1( 1,2 个下标)。如果扩张在温度为300K的恒温过程,则: (a) 膨胀气体所对外做的功? 和 (b)”熵”的变化? (c)如果膨胀是可逆绝热而不恒温过程, 气体”熵”的变化是多少? 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%) “熵”的变化是多少在下列所述之环境: (a) 任何一个可逆的封闭循环 和 (b)不可逆转过程, 最後的T和V和一开始的相同。 10. Consider a damped simple harmonic motion with the total force EF=-kx-bv (E表Sigma打不出来),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%) 用总力把减弱的简谐运动看作 EF=- kx - bv , k是弹簧中的"力常数", x是位移, v是速度, b减弱的常数。请写出和解出牛顿第二定律运动的微分方程式。 11.Good luck!!!and Happy NEW YEAR! 祝好运!!!新年快乐! -- 此生 此爱 此刻挥霍 挥霍我的色彩 在你的天空 --

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