普通物理

注意：

1. 本條目為個人之重點筆記，非完整講義。
2. 請在偏好設定中關閉章節編號。
3. 本教材以 General Physics for Sciences and Engineering Faculties e.10 (Serway, Jewett)

12

• Equilibrium ($\Sigma F=0,\Sigma \tau =0$)

14 流體力學 Fluid Mechanics

例題: 10 16 21 29 34 38 44 46 48 49
流體力學是研究流體運動及受力的物理分支。流體分為氣液兩種。

氣體 Gases	液體 Liquid
均勻分布整個空間 Fill their containers	佔據空間中最低的地方，具有固定體積 Occupies the lowest possible regions
relatively incompressible 相對不可壓縮	compressible (whose $\rho$ is strongly dependent on T, P)
molecules with short-ranged bond 具有分子間引力	molecules hardly interact with one another 分子間幾乎不互相作用

Pressure in fluid

• Pressure $P=r{\frac {F}{A}}$ 壓力為力面之商。
  • Pascal (SI, $1Pa={\frac {1N}{m^{2}}}$, 中文稱帕斯卡
  • Torr (=mmHg, 中文稱托)
  • Bar (=100kPa, 中文稱巴，氣象學常用)。
• Density 密度 $\rho ={\frac {m}{\text{V}}}$
  

$${\begin{aligned}{\text{in Equilibrium,}}\\P_{1}\cdot A-(P+dP)A-\rho (Ady)g&=0\\-dP-\rho gdy&=0\\\int _{P_{1}}^{P_{2}}dP&=\int _{y_{1}}^{y_{2}}\rho gdy\\{\text{for Liquid, the density is const.}}\\\Delta P=-\rho g\int dy=-\rho g\Delta y\\P=P_{0}+\rho gh\\{\text{for Gases, the density is variable.}}\\{\frac {\rho }{\rho _{0}}}={\frac {P}{P_{0}}}\Rightarrow \rho =P\cdot {\frac {\rho _{0}}{P_{0}}}\\dP=-\rho gdy=-P{\frac {\rho _{0}}{P_{0}}}gdy\\\Rightarrow {\frac {dP}{P}}&=-{\frac {\rho _{0}}{P_{0}}}gdy\\&=-a\cdot dy{\text{, where a is 0.116 }}km^{-1}\\\int _{P_{0}}^{P}{\frac {dP}{P}}=-a\int _{y_{0}}^{y}dy\\lnP-lnP_{0}=-ay\\P=P_{0}\cdot \exp(-{\frac {\rho _{0}}{P_{0}}}gy)\end{aligned}}$$

• Pascal's law:${\text{P is const, }}{\frac {F_{1}}{A_{1}}}={\frac {F_{2}}{A_{2}}}$

Fluid Dynamics流體動力學

• Ideal Fluid理想液體:
  • luminar flow:
    • 不旋轉、不可壓縮、穩定流動、
  • streamline流線, 類似磁力線的東西
    • smooth path 物體在流體中時沿平滑路徑，即流線運動
    • no crossing 兩條流線不相交
    • 與流速的關係：速度方向即流線切向，大小即流線密度。

• Continuity equation for an incompressible fluid: 任一處密度相等，且任一截面單位時間流過質量相等。

$\rho \cdot A\cdot v{\text{ is const., so }}A\cdot v{\text{ is const.}}$

15 Oscillatory Motion

16 Wave Functio

8,14,18,22,30,37,42,51,57,60

16.1 type of waves

• Transverse Wave 橫波
• Longitudinal Wave 縱波
• Surface wave 表面波:Particles move along a circular trace, i.e. it has both perpendicular wave and parallel wave components.

16.2 Wave Funtio du Travelling Wave

• 匴法：平移回t=0時位置

$y_{t=0}=f(x)$，給出t=0時原本波形。 $y(x,t)=f(x_{t=0})=f(x-vt)$, where the velocity is const. (注意 v, t的正負)

• 週期波：以Sinusoidal Wave弦波為舉例：

$y(x,t=0)=f(x)=A\sin(ax)$ $y({\frac {\lambda }{2}},0)=0\Rightarrow a={\frac {2\pi }{\lambda }}$ $y(x,t\neq 0)=f(x-vt)=A\sin[{\frac {2\pi }{\lambda }}\cdot (x-vt)]$，又 $v={\frac {\lambda }{T}}$，則
$y(x,t)=A\sin[2\pi ({\frac {x}{\lambda }}-{\frac {t}{T}})]=A\sin(2\pi \lambda ^{-1}-\omega t+\phi )$ (因為 $\omega ={\frac {2\pi }{T}}$

18 Temperature

• from Macroscopic view:
  • Thermodynamics - eto empirical laws
  • Uses scalars (P, V, T, m)
• from Microscopic view:
  • Kinetic theory of gas - Newton's law is applied to describe the motion of molecule of system.
  • Uses vectors (r, v, a)

18.1 Temperature

• Thermal contact (熱交換):Energy can exchange between the 2 system
• Thermal equilibrium (熱平衡): the 2 system dont exchange energy by heat or electromagnetic radiation.
• Zeroth Law of Thermodynamics: A and C are in ThEq, B and C are in ThEq then A and B are in ThEq.

18.2 Thermometres

氣相液相固相的溫度計。

19 the First Law of Thermodynamics

圈題目：6 14 15 22 23 34 35 40 44 45

19.2 Heat and Internal Energy

• Heat 熱 - ecce energia.