Re: [題目] 5題普物~

[nightkid (固有結界：無限の劍製)]

※ 引述《hsujay0416 (囧囧有神)》之銘言：
: 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.

         I=∫r^2 dm

:    (b) When the pendulum vibrates with a small amplitude, calculate its
:        frequency.

         derive S.H.M.
         Hint: (1)calculate "torque" first
               (2)when it vibrates with a small amplitude, sinθ→θ.

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

      first of all, you need to know what is wave equation.
      then, try to find everything you need by yourself.
      Hint: (1)dm = μdx
            (2)v=dx/dt

      Note: if your text book is written by Harris Benson, the derivation of
            this question is in your text book. please check CH.15~17

: 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)

         please read the chapter which is talking about Bulk modulus.

         if your text book is written by Harris Benson, it would in CH.17or18.

:    (b) Estimate the density of the air at the room temperature.

         PV=NRT

:    (c) Calculate the speed of the sound wave.

         please read the chapter which is talking about Bulk modulus.

         if your text book is written by Harris Benson, it might in CH.17or18.

: 4.  Entropy
:    (a) Write down the definition of the entropy change.

         please read your text book.

         if your text book is written by Harris Benson, please read CH.19,21

:    (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.

         please read your text book.

         again, if your text book is written by Harris Benson, please find

         the title "free-expansion"

:    (c) What is the entropy change?

         if you do read all these things, I think it's a piece of cake.

: 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?

         insert it, and check it.

         Hint: maybe you need to read the chapter which is talking about the
               heat engine.
               the same, if your book is written by Harris Benson, please read
               CH.21.

:    (b) Use this engine to show that the 2nd law of the thermodynamics will be
:        violated.

         just do it.

: 請大家幫忙一下
: 3Q~

我已經幫你了
不要客氣~

--
        I am the bone of my paper. Pen is my body, and ink is my blood.
                 I have finished over a thousand assignments.
                     Unknown to pass. Nor known to fail.
                  Have withstood pain to take many midterms.
                 Yet, those hands will never write anything.
                      So as I pray, Unlimited homeworks.

--
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◆ From: 140.115.31.196
推 xgcj:...
不小心打太多錯字
※ 編輯: nightkid        來自: 140.115.31.196       (01/05 19:06)
推 hank780420:推薦這個無限的作業製  這次我會寫掉幾張A4呢(抖
推 HDT:好人夜童大 為啥問你Lagrangian和Hamiltonian都說不肯教我
→ nightkid:我有教你啊 看課本
推 HDT:...痾= =
推 a0184030:我笑了 打這麼多字真是辛苦你了XDDDD