physics-class-11-unit-11-chapter-04-microscopic-and-macroscopic-approach-to-thermal-properties-l-1-4-qj6i2wgl9oe

### <Success style="font-size:25px"> Microscopic And Macroscopic Approach To Thermal Properties L-1 </Success>
### <primary style="font-size:24px"> Average Distribution </primary>
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- Steam Point : Highest of Water

- Ice point : Lowest of water

- We can measure anything with respect to these two temperature in our Celsius scale.

- Average : a huge number of particles, $10^{23}$.

- In mechanics, each molecule described by Newton's laws: $m \frac{d^2 \vec{x}}{dt^2} = \vec {F}$

- $3 \times 10^{23} \rightarrow$ average description.
	
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<footer style = "font-size: 18px">Heat $\rightarrow$ Temprature $\rightarrow$ <span style = "color:blue"> Average Distribution </span> $\rightarrow$ Microscopic and Macroscopic Levels $\rightarrow$ Ideal Gas </footer>

### <Success style="font-size:25px"> Microscopic And Macroscopic Approach To Thermal Properties L-1 </Success>
### <primary style="font-size:24px"> Microscopic and Macroscopic Levels </primary>
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- Kinetic theory

- (i) Distribution

- (ii) Gas molecule $\rightarrow$ velocities

- Distribution of velocity will give me average properties which will be related to kinetic energy.

- Thermodynamics language is a coarse-grained description.

- In the macroscopic level we will consider the measurable quantities.

- P, T $\rightarrow$ Intensive

- V $\rightarrow$ Extensive
	
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<footer style = "font-size: 18px">Temprature $\rightarrow$ Average Distribution $\rightarrow$ <span style = "color:blue"> Microscopic and Macroscopic Levels </span> $\rightarrow$ Ideal Gas $\rightarrow$ Limiting Situation </footer>

### <Success style="font-size:25px"> Microscopic And Macroscopic Approach To Thermal Properties L-1 </Success>
### <primary style="font-size:24px"> Limiting Situation </primary>
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- de Broglie wavelength: $\lambda = \frac{h}{p}$

- $\lambda = \frac{h}{\sqrt{2mkT}}$

- a $\rightarrow$ container ofV, N

- $(\frac{V}{N})^{1/3} = a$

- $a>> \lambda$

- Let us assume that the average kinetic energy of a molecule:$\frac{p^2}{2m} \sim kT$

- $p \sim \sqrt{2mkT}$

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<footer style = "font-size: 18px">Microscopic and Macroscopic Levels $\rightarrow$ Ideal Gas $\rightarrow$ <span style = "color:blue"> Limiting Situation </span> $\rightarrow$ Limiting Situation $\rightarrow$ Limiting Situation </footer>

### <Success style="font-size:25px"> Microscopic And Macroscopic Approach To Thermal Properties L-1 </Success>
### <primary style="font-size:24px"> Kinetic Energy of Gas </primary>
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- Kinetic Energy of Gas : Microscopic description.

- (i) Molecules are moving in all average directions.

- (ii) Points particles size, smaller than interatomic distance.

- (iii) Any interaction $\rightarrow$ collisions between two molecules.
	
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<footer style = "font-size: 18px">Limiting Situation $\rightarrow$ Limiting Situation $\rightarrow$ <span style = "color:blue"> Kinetic Energy of Gas </span> $\rightarrow$ Classical Motion $\rightarrow$ Distribution </footer>

### <Success style="font-size:25px"> Microscopic And Macroscopic Approach To Thermal Properties L-1 </Success>
### <primary style="font-size:24px"> Classical Motion </primary>
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- Consider classical motion, so all these molecules satisfy Newton's laws of motion.

- Collisions are elastic collisions which are all dictated by the classical mechanics.

- Homogeneous : density is uniform.

- Velocities will be having three components ($v_x, v_y, v_z$).

- We will consider complete isotropic.

- Equilibrium is independent of time.

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<footer style = "font-size: 18px">Limiting Situation $\rightarrow$ Kinetic Energy of Gas $\rightarrow$ <span style = "color:blue"> Classical Motion </span> $\rightarrow$ Distribution $\rightarrow$ Maxwell's Velocity Distribution </footer>

### <Success style="font-size:25px"> Microscopic And Macroscopic Approach To Thermal Properties L-1 </Success>
### <primary style="font-size:24px"> Distribution </primary>
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- $x \rightarrow - \infty$ to $\infty$

- Average value: $\langle x \rangle = \int x P(x) dx$

- Total probability: $\int_{-\infty}^{\infty} P(x) dx=1$

- P(x)=Ne
	
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<footer style = "font-size: 18px">Kinetic Energy of Gas $\rightarrow$ Classical Motion $\rightarrow$ <span style = "color:blue"> Distribution </span> $\rightarrow$ Maxwell's Velocity Distribution $\rightarrow$ Ideal Gas in a Container </footer>

### <Success style="font-size:25px"> Microscopic And Macroscopic Approach To Thermal Properties L-1 </Success>
### <primary style="font-size:24px"> Maxwell's Velocity Distribution </primary>
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- Velocity components are $v_x, v_y, v_z$

- $v=\sqrt{v_x^2 + v_y^2 + v_z^2}$

- $P(v_x)P(v_y)P(v_z) dv_x dv_y dv_z$

- $\sim Ae^{ -a(v_x^2 + v_y^2 + v_z^2)} dv_x dv_y dv_z$

- Speed Distribution:

- $P(v)dv = Av^2 e^{-bv^2} dv$

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<footer style = "font-size: 18px">Classical Motion $\rightarrow$ Distribution $\rightarrow$ <span style = "color:blue"> Maxwell's Velocity Distribution </span> $\rightarrow$ Ideal Gas in a Container $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> Microscopic And Macroscopic Approach To Thermal Properties L-1 </Success>
### <primary style="font-size:24px"> Ideal Gas in a Container </primary>
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- Random motion of the particles inside a container.

- $PV = \frac{1}{3} m N \bar v^2$

- Euation of state of a gas.
 
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<footer style = "font-size: 18px">Distribution $\rightarrow$ Maxwell's Velocity Distribution $\rightarrow$ <span style = "color:blue"> Ideal Gas in a Container </span> $\rightarrow$ Thank You $\rightarrow$  </footer>