physics-class-11-unit-13-chapter-02-equipartiton-of-energy-l-2-3-x-vfkp23jgg

### <Success style="font-size:25px"> Equipartiton Of Energy L-2 </Success>
### <primary style="font-size:24px"> Recap </primary>
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- $P = \frac{1}{3} \frac{m N}{L^3} v_{r m s}^2$ $v_{r m s}^2$

- $P = \frac{1}{3} \rho v_{r m s}^2$

- $P V=\frac{1}{3} M v_{r m s}^2=\frac{1}{3} m N v_{r_{m s}}^2$ $=\frac{1}{N} \sum_{i=1}\left(v_i^x\right)^2$  $+\left(v_i^y \right)^2$

- How do you relate it temp.

- Ideal gas eqn, of state PV=nRT

- PV=$Nk_BT$

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<footer style = "font-size: 18px"> $\rightarrow$ Equipartition of Energy $\rightarrow$ <span style = "color:blue"> Recap </span> $\rightarrow$ Equipartition of Energy $\rightarrow$ Equipartition of Energy </footer>

### <Success style="font-size:25px"> Equipartiton Of Energy L-2 </Success>
### <primary style="font-size:24px"> Equipartition of Energy </primary>
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- $\frac{1}{2} m\left(3 v_x^2\right)=\frac{3}{2} k_BT$

- $\frac{1}{2} m v_x^2=\frac{1}{2} k_BT$

- $\frac{1}{2} N{m v_2^2} =\frac{N}{2} K_i$

- $\frac{1}{2} m v_y^2=\frac{1}{2} k_BT$

- $ v^2  =v_x^2+v_y^2+v_z^2  =3 v_x^2$

- Three components of velocity

- E = $\frac{1}{2}k_BT$

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<footer style = "font-size: 18px">Recap $\rightarrow$ Equipartition of Energy $\rightarrow$ <span style = "color:blue"> Equipartition of Energy </span> $\rightarrow$ Harmonic Oscillators $\rightarrow$ Harmonic Oscillators </footer>

### <Success style="font-size:25px"> Equipartiton Of Energy L-2 </Success>
### <primary style="font-size:24px"> Harmonic Oscillators </primary>
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- $N \longrightarrow 3 \text { dimensions } \longrightarrow v_i^x, v_i^y, v_i^z $

- $ \frac{1}{2} N k_B T+\frac{1}{2} N k_B T+\frac{1}{2} N k_B T=\frac{3}{2} N k_B T$

- $E=\frac{p^2}{2 x}+\frac{1}{2} k x^2$

- $\langle E\rangle=k_B T$

- $\langle E\rangle=3Nk_B T$

- $f = - kx$

- $V =\frac{1}{2}kx^2$

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<footer style = "font-size: 18px">Equipartition of Energy $\rightarrow$ Equipartition of Energy $\rightarrow$ <span style = "color:blue"> Harmonic Oscillators </span> $\rightarrow$ Harmonic Oscillators $\rightarrow$ Rotational Kinetic Energy </footer>

### <Success style="font-size:25px"> Equipartiton Of Energy L-2 </Success>
### <primary style="font-size:24px"> Harmonic Oscillators </primary>
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- $ C_V = \frac{d E}{d T} $
 
- $ C_p=Lt_{\Delta T \rightarrow 0} \frac{\Delta E}{\Delta T}$

- <span style="color:blue">For ideal Gas</span>

- $C_p-C_r=R$

- $C_V=\frac{3}{2} N k_{ B}$

- <span style="color:blue">Harmonic Oscillator :</span>

- $C_V = 3 N k_B$

- <span style="color:green">Ideal Gas : Monoatomic</span>

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<footer style = "font-size: 18px">Equipartition of Energy $\rightarrow$ Harmonic Oscillators $\rightarrow$ <span style = "color:blue"> Harmonic Oscillators </span> $\rightarrow$ Rotational Kinetic Energy $\rightarrow$ Polyatomic </footer>

### <Success style="font-size:25px"> Equipartiton Of Energy L-2 </Success>
### <primary style="font-size:24px"> Polyatomic </primary>
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-  Rigid body 
 
- 6 degrees of freedom

- $3 \rightarrow$ translational

- $3 \rightarrow$ rotational

- Rigid body approximation

- $10^{23}$ particles

- $\rightarrow N 6\frac{1}{2}kT = 3NKT$
	
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<footer style = "font-size: 18px">Harmonic Oscillators $\rightarrow$ Rotational Kinetic Energy $\rightarrow$ <span style = "color:blue"> Polyatomic </span> $\rightarrow$ Pressure $\rightarrow$ Thermal Equation </footer>