3. Thermal Physics

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# 3.1 Thermal concepts
## Temperature and absolute temperature
There have two commonly used measurment of temperature, one is **Celsius(摄氏度)** and the other one is **Kelvin（开氏度）**
The **temperature difference** between them is **same** ${\Delta K}={\Delta C}$
Absolute zero is 0K whcih is -273C

## Heat(Internal Energy)
>**Heat** is energy that is **transferred** from one body to another as a 
result of a **difference in temperature**.

>**Internal energy** is the **total** random **kinetic energy** of the 
particles of a substance, **plus** the total inter-particle **potential 
energy** of the particles.

>The **heat**(temperature) is the **only** determintion of the **kenetic energy**(温度是衡量动能的唯一标准)

 

##  specific heat capacity 
**Specific heat** capacity follow the formula:
$$Q=mc{\Delta T}$$
Q is energy(heat), m is mass, ${\Delta T}$ is Temperature change and c is specific heat capacity.

- To define this equation, it means that suppose there's a object A have specific heat capacity c and it required Q energy to raise it's temperature **1K(C)**

- Different substances have different specific heat capacities because of different physical properties
## Change of phase
When heating some substances it might not necessarily increase temperature but change phase
- melting(solid to liquid)
- freezing(liquid to solid)
- vaporisation/boiling(liquid to gas)
- condensation(gas to liquid)
- Sublimation（solid to gas）
- condensation(gas to solid)

## Specific latent heat
Specific latent heat follow the formula:
$$Q = mL$$
In this case the L can be replaced by L~V~(vaporisation) and L~F~(fusion)
- specific latent heat of fusion: The amount of heat required to change **mkg** of a substance from **solid** **to liquid** without any change in temperature.
- Specific latent heat of vaporization: The amount of heat required to change **mkg** of a substance from **liquid to gas** without any change in temperature.
# 3.2Modelling a gas
## The Avogadro constant
Avogadro constant $N_A$ is a **experimental constant** that measurment the number of particle in one **mole** of substance, which $N_A=6.022\times 10^{23}mol^{-1}$
mole is measured by the amnount of particle carried by 12g of Carbon-12 which repersent as $n$
$$n={\frac{N}{N_A}}$$
n is mol number, N is number of particle and $N_A$ is avogadro constnt
## Pressure
Pressure is defined as the **normal force** applied **per unit area** which followed the equation:
$$p={\frac{F}{A}}$$
p is pressure F is force and A is area.
If the force dose **not vertically** acting at an object, then should use the equation:
$$p=\frac{Fcosθ}{A}$$
p in **non-closed** condition should be equal to 1atm which is $1.013 × 10^{5}Pa$ on Earth
## Ideal gas
An ideal gas is a theoretical model of a gas which should follow the rules that:
- The molecules are **point particles**, each with **negligible volume**.
- The molecules obey the laws of mechanics.
- There are **no forces** between the molecules except when the molecules collide.
- The duration of a collision is **negligible** compared to the time between collisions.
- The collisions of the molecules with each other and with the container walls are **elastic**.
- Molecules have a **range of speeds** and **move randomly**.
> The real gas at high temperature and low pressure will close to ideal gas
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An ideal gas should followed the equation:
$$PV=nRT$$
P is pressure, V is volume, n is mole number, R is ideal gas constant($8.31Jmol^{-1}K^{-1}$) and T is temperature
## The Boltzmann equation
$$E_{avg}=\frac{3}{2}k_bT$$
This is measurment of average kenetic energy in ideal gas, and $k_b$ means $\frac{R}{N_A}$ which is $1.38\times10^{−23}JK{−1}$
Therefore the average internal energy would be 
$$U=\frac{3}{2}pV$$