physics-class-11-unit-13-chapter-01-kinetic-theory-of-gases-equation-of-ideal-gas-l-01-3-0l39r8d6yzg

### <Success style="font-size:25px"> Kinetic Theory Of Gases Equation Of Ideal Gas L-01 </Success>
### <primary style="font-size:24px"> Probability distribution </primary>
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- **Normalization**

- $\int_{-\infty}^{\infty} P(x) d x=1$

- $ \bar{x}=\int_{-\infty}^{\infty} x P(x) d x$

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<footer style = "font-size: 18px"> $\rightarrow$ Kinetic Theory of Gases Equation of Ideal Gas $\rightarrow$ <span style = "color:blue"> Probability distribution </span> $\rightarrow$ What did We Learn? $\rightarrow$ Ideal Gas </footer>

### <Success style="font-size:25px"> Kinetic Theory Of Gases Equation Of Ideal Gas L-01 </Success>
### <primary style="font-size:24px"> What did We Learn? </primary>
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- $P(v_x) d v_x=A e^{-\alpha v_x^2} d v_x$

- $v_x \rightarrow v_x+d v_x$

- $\bar{v_x} = 0$, RMS velocities.

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

- $v \Longrightarrow v+d v $

- $P(v) d v=B v^2 e^{-a v^2} d v$

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![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-11-unit-13-chapter-01-kinetic-theory-of-gases-equation-of-ideal-gas-l-01_3-0l39r8d6yzg-05.jpg)

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<footer style = "font-size: 18px">Kinetic Theory of Gases Equation of Ideal Gas $\rightarrow$ Probability distribution $\rightarrow$ <span style = "color:blue"> What did We Learn? </span> $\rightarrow$ Ideal Gas $\rightarrow$ Confined a Volume </footer>

### <Success style="font-size:25px"> Kinetic Theory Of Gases Equation Of Ideal Gas L-01 </Success>
### <primary style="font-size:24px"> Ideal Gas </primary>
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- High T, low density limit of "real" gas.

- $\{P} V=$ Constant

- T absolute Scale

- $ P \propto T$

- $T=t_{cell}+273.16$

- $PV = nRT$

- T = 0, absolute Zero

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<footer style = "font-size: 18px">Probability distribution $\rightarrow$ What did We Learn? $\rightarrow$ <span style = "color:blue"> Ideal Gas </span> $\rightarrow$ Confined a Volume $\rightarrow$ Elastic Collision </footer>

### <Success style="font-size:25px"> Kinetic Theory Of Gases Equation Of Ideal Gas L-01 </Success>
### <primary style="font-size:24px"> Confined a Volume </primary>
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- Ideal Gas : Confined in a Volume.

- Microscopic approach $\rightarrow$ Macroscopic

- Volume $\rightarrow$ Cube :  $L^3$

- Momentum transferred

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<footer style = "font-size: 18px">What did We Learn? $\rightarrow$ Ideal Gas $\rightarrow$ <span style = "color:blue"> Confined a Volume </span> $\rightarrow$ Elastic Collision $\rightarrow$ Momentum Transferred </footer>

### <Success style="font-size:25px"> Kinetic Theory Of Gases Equation Of Ideal Gas L-01 </Success>
### <primary style="font-size:24px"> Momentum Transferred </primary>
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- ${F=\frac{1}{3} \frac{m}{L} \sum_{i=1}^N \vec{v}_i^2}$

- $\vec{v}_i^2=(v_i^x)^2+(v_i^y)^2+(v_i^z)^2$

- $=\frac{1}{3} \frac{mN}{L}(\frac{1}{N} \sum_{i=1}^N v_i^2)$

- **Mean Square**

- $v_{\text {rms }}^2=\frac{1}{3} \frac{m N}{L} v_{r m s}^2$

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<footer style = "font-size: 18px">Momentum Transferred $\rightarrow$ Isotropy $\rightarrow$ <span style = "color:blue"> Momentum Transferred </span> $\rightarrow$ Pressure $\rightarrow$ Momentum Transferred </footer>

### <Success style="font-size:25px"> Kinetic Theory Of Gases Equation Of Ideal Gas L-01 </Success>
### <primary style="font-size:24px"> Momentum Transferred </primary>
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- <span style="color:blue">1 mole</span>

- $P V=N k_B T=\frac{1}{3} m N v_{\text {rMs }}^2$

- $\frac{1}{3} m V_{r m s}^2=k_B T$

- Total Translational K.E of the molecule

- $\frac{1}{2} m v_{r_{M S}}^2=\frac{3}{2} k_B T$
	
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![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-11-unit-13-chapter-01-kinetic-theory-of-gases-equation-of-ideal-gas-l-01_3-0l39r8d6yzg-13.jpg)

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<footer style = "font-size: 18px">Momentum Transferred $\rightarrow$ Pressure $\rightarrow$ <span style = "color:blue"> Momentum Transferred </span> $\rightarrow$ Dulong-Petit Law $\rightarrow$ Equipartition of Energy </footer>

### <Success style="font-size:25px"> Kinetic Theory Of Gases Equation Of Ideal Gas L-01 </Success>
### <primary style="font-size:24px"> Dulong-Petit Law </primary>
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- $PV=\frac{1}{3} m N v_{\text {rms }}^2$
 
- $ \frac{1}{2} m v_{r m s}^2=k_B T = \frac{1}{2} I \omega^2$

- Total Translational $\rightarrow$ (Monoatomic) K.E

- $\varepsilon_p=\frac{p^2}{2 m} = p c$

- Translational: $\varepsilon_{total} = \frac{1}{2} m N{V^2}_{rms} $

- $ PV=\frac{2}{3} E$

- $\frac{1}{2} m v_{\text {rms }}^2=\frac{3}{2} k_B T$

- $\varepsilon_{\text {total }} = \quad \frac{3 N}{2} k_B T \Rightarrow \frac{\partial \varepsilon_{\text {total }}}{\partial T}=\frac{3 N}{2} k_B$

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![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-11-unit-13-chapter-01-kinetic-theory-of-gases-equation-of-ideal-gas-l-01_3-0l39r8d6yzg-14.a.jpg)

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<footer style = "font-size: 18px">Pressure $\rightarrow$ Momentum Transferred $\rightarrow$ <span style = "color:blue"> Dulong-Petit Law </span> $\rightarrow$ Equipartition of Energy $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> Kinetic Theory Of Gases Equation Of Ideal Gas L-01 </Success>
### <primary style="font-size:24px"> Equipartition of Energy </primary>
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- $\frac{1}{2} m v^2=\frac{3}{2} k T = \frac{1}{2} kT +\frac{1}{2}$$kT+\frac{1}{2} kT$

- $\frac{1}{2} m \vec v_x^2=\frac{1}{2} m \vec{v}_y^2=\frac{1}{2} m \vec v_z^2 $

- $ \frac{1}{2} m \vec{v}_x^2=\frac{1}{2} k T \rightarrow$ Each degrees of freedom.

- $\frac{1}{2} k T \rightarrow$ Equipartition of energy
	
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![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/physics-class-11-unit-13-chapter-01-kinetic-theory-of-gases-equation-of-ideal-gas-l-01_3-0l39r8d6yzg-15.jpg)

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<footer style = "font-size: 18px">Momentum Transferred $\rightarrow$ Dulong-Petit Law $\rightarrow$ <span style = "color:blue"> Equipartition of Energy </span> $\rightarrow$ Thank You $\rightarrow$  </footer>