[題目] 5題普物~

[hsujay0416 (囧囧有神)]

1. Consider a pendulum of the shape of a (solid) triangle. Its three
   edges have the same length 1m. The mass of the pendulum is 1kg. The pendulum
   can rotate around its tip.

   (a) Calculate the moment of the inertia.
   (b) When the pendulum vibrates with a small amplitude, calculate its
       frequency.

2.  A string with the mass per unit length μ is under the tension τ.
   Derive the wave equation for the transverse waves.

3.  Consider the air as an ideal gas with the constant heat capacity
   5R/2 per mol, where R=8.3J/mol*K. When the sound wave is propagating through
   the air, the air is compressed or expanded.

   (a) Assume that the air is compressed without exchanging heat with the
       environment (adiabatic process). Calculate the bulk modulus
       B = -V^-1 * (dV/dP)      (d為偏微分)
   (b) Estimate the density of the air at the room temperature.
   (c) Calculate the speed of the sound wave.

4.  Entropy

   (a) Write down the definition of the entropy change.
   (b) One mole of the ideal gas undergoes the free expansion from 24.4L,
       1atm (298K) to 73.2L. Calculate the heat and the work of this process.
   (c) What is the entropy change?

5.  Suppose that an alien brings you a wonderful engine. In each cycle
   it extracts heat Q1 = 700J from T1 = 350K heat reservoir, releases heat
   Q2 = -375J to T2 = 325K heat reservoir, and Q3 = -250J to T3 = 300K heat
   reservoir.

   (a) Check the Clausius theorem to see whether it still valids?
   (b) Use this engine to show that the 2nd law of the thermodynamics will be
       violated.



請大家幫忙一下
3Q~

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