### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Mean Freepath and Non Ideal Gas </primary> <hr> <main> <div style='float: left; width:100%; text-align:left; font-size:30px;'> </div> <div style='float: right; width:0%;'>  </div> </main> <hr> <footer style = "font-size: 18px"> $\rightarrow$ $\rightarrow$ <span style = "color:blue"> Mean Freepath and Non Ideal Gas </span> $\rightarrow$ Recapitulate $\rightarrow$ Recapitulate </footer>

### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Recapitulate </primary> <hr> <main> <div style='float: left; width:99%; text-align:left; font-size:30px;'> - $C_v , C_p$: heat Capacity - $C_p-C_v=R$, for an ideal Gas. - $ E=\frac{p^2}{2m}$ </div> <div style='float: right;width:0%;'>   </div> </main> <hr> <footer style = "font-size: 18px"> $\rightarrow$ Mean Freepath and Non Ideal Gas $\rightarrow$ <span style = "color:blue"> Recapitulate </span> $\rightarrow$ Recapitulate $\rightarrow$ Diatomic Molecules </footer>

### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Recapitulate </primary> <hr> <main> <div style='float: left; width:99%; text-align:left; font-size:30px;'> - Equipartition of Energy: $\frac{1}{2} kT$ - <span style="color:blue">Monoatomic Gases</span>: $\frac{3}{2}Nk_bT \quad C_p=\frac{5}{2} R$ - $E=\frac{p^2}{2 m}+\frac{1}{2} {k x^2}$ - $C_v=\frac{3}{2}R$ - $E=Nk_BT$ - Polyatomic $\left(3+f\right) R$ </div> <div style='float: right;width:0%;'>   </div> </main> <hr> <footer style = "font-size: 18px">Mean Freepath and Non Ideal Gas $\rightarrow$ Recapitulate $\rightarrow$ <span style = "color:blue"> Recapitulate </span> $\rightarrow$ Diatomic Molecules $\rightarrow$ Mean Free Path </footer>

### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Diatomic Molecules </primary> <hr> <main> <div style='float: left; width:50%; text-align:left; font-size:30px;'> - Translational + Potential + Vibrational - $\frac{3}{2} N k_B T+\frac{1}{2} \times 2 N \times k_B T=\frac{5}{2} N k_B T$ - Rotational KE : $\frac{1}{2} I_1 \omega^2$ - $ C_V=\frac{5}{2} R $ - A vibrational mode corresponds to a situation like a simple harmonic oscillator. - $C_V=\left(\frac{5}{2}+f\right) k_B N$ </div> <div style='float: right; width:50%;'>  </div> </main> <hr> <footer style = "font-size: 18px">Recapitulate $\rightarrow$ Recapitulate $\rightarrow$ <span style = "color:blue"> Diatomic Molecules </span> $\rightarrow$ Mean Free Path $\rightarrow$ Mean Free Path </footer>

### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Mean Free Path </primary> <hr> <main> <div style='float: left; width:99%; text-align:left; font-size:30px;'> - Average distance travelled by a gas molecule between two successive collision. - Average Speed of a molecule: $\bar{v}$ - Distance travelled by this molecule in time $\Delta t$ $\bar{v} \Delta t$ - Diameter : d </div> <div style='float: right;width:0%;'>  </div> </main> <hr> <footer style = "font-size: 18px">Recapitulate $\rightarrow$ Diatomic Molecules $\rightarrow$ <span style = "color:blue"> Mean Free Path </span> $\rightarrow$ Mean Free Path $\rightarrow$ Average Distance </footer>

### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Mean Free Path </primary> <hr> <main> <div style='float: left; width:50%; text-align:left; font-size:30px;'> - Hard sphere - Assume all other molecules are static. - Total number of Collisions over a time $\Delta t$= n $\pi d^2\bar{v} \Delta t$ </div> <div style='float: right; width:50%;'> <!----> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/976788a8-1533-49fa-065d-1118ddd31400/public" width="50%" > </main> <hr> <footer style = "font-size: 18px">Diatomic Molecules $\rightarrow$ Mean Free Path $\rightarrow$ <span style = "color:blue"> Mean Free Path </span> $\rightarrow$ Average Distance $\rightarrow$ Average Distance </footer>

### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Average Distance </primary> <hr> <main> <div style='float: left; width:99%; text-align:left; font-size:30px;'> - $\tau=\frac{1}{n \pi d^2\bar v}$ - $l=\bar{v} \tau= \frac{1}{c n \pi d^2} \longrightarrow c=\sqrt{2}$ </div> <div style='float: right;width:0%;'>  </div> </main> <hr> <footer style = "font-size: 18px">Mean Free Path $\rightarrow$ Mean Free Path $\rightarrow$ <span style = "color:blue"> Average Distance </span> $\rightarrow$ Average Distance $\rightarrow$ Van der Waals Equation of State </footer>

### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Average Distance </primary> <hr> <main> <div style='float: left; width:99%; text-align:left; font-size:30px;'> - Hard sphere, strong repulsion. - Weak attractive interaction electrostatics. - Lenard Jones potential. - $PV= n RT$ </div> <div style='float: right;width:0%;'>  </main> <hr> <footer style = "font-size: 18px">Mean Free Path $\rightarrow$ Average Distance $\rightarrow$ <span style = "color:blue"> Average Distance </span> $\rightarrow$ Van der Waals Equation of State $\rightarrow$ Identical Particles </footer>

### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Van der Waals Equation of State </primary> <hr> <main> <div style='float: left; width:99%; text-align:left; font-size:30px;'> - $\left(P+\frac{a}{v^2}\right)(v-b)=RT$ - For one mole of real gas * Average attractive force * Correction to the volume </div> <div style='float: right;width:0%;'>  </div> </main> <hr> <footer style = "font-size: 18px">Average Distance $\rightarrow$ Average Distance $\rightarrow$ <span style = "color:blue"> Van der Waals Equation of State </span> $\rightarrow$ Identical Particles $\rightarrow$ Identical Particles </footer>

### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Identical Particles </primary> <hr> <main> <div style='float: left; width:50%; text-align:left; font-size:30px;'> - Two of them - Each molecule: Excluded volume - $\rightarrow \frac{4}{3} \pi(d)^3=$ V excluded - $=8 \cdot \frac{4}{3} \pi\left(\frac{d}{2}\right)^3=$ 8 $V_{mol}$ </div> <div style='float: right; width:50%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/d3eb4590-0964-4f27-b9d3-19d3141f8100/public" width="50%" > <!----> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Average Distance $\rightarrow$ Van der Waals Equation of State $\rightarrow$ <span style = "color:blue"> Identical Particles </span> $\rightarrow$ Identical Particles $\rightarrow$ Identical Particles </footer>

### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Identical Particles </primary> <hr> <main> <div style='float: left; width:50%; text-align:left; font-size:30px;'> - Identical particles - Average excluded volume - volume: $\frac{1}{2}\left(8 V_{\text {mol }}\right)$ - $b=4 v_{\text {mol }}$ - $\rightarrow b \propto 4 V_{\text {mol }}$ - $\rightarrow \frac{4}{3} \pi(d)^3=V_{\text {excluded }}$ - $ =8 \cdot \frac{4}{3} \pi\left(\frac{d}{2}\right)^3=8 V_{\text {mol }}$ </div> <div style='float: right; width:50%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/d3eb4590-0964-4f27-b9d3-19d3141f8100/public" width="50%" > <!----> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Van der Waals Equation of State $\rightarrow$ Identical Particles $\rightarrow$ <span style = "color:blue"> Identical Particles </span> $\rightarrow$ Identical Particles $\rightarrow$ Isotherms </footer>

### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Identical Particles </primary> <hr> <main> <div style='float: left; width:99%; text-align:left; font-size:30px;'> - (i) Weak attractive force - (ii) Repulsion from the wall - $p=\frac{RT}{V-b} -\frac{a}{V_2}$ - $\left(p+\frac{a}{v^2}\right)(v-b)=R T \quad n=\frac{N}{V}$ - $\rightarrow$ Number of molecules hitting the wall $\propto n$. </div> <div style='float: right;width:0%;'>  </div> </main> <hr> <footer style = "font-size: 18px">Identical Particles $\rightarrow$ Identical Particles $\rightarrow$ <span style = "color:blue"> Identical Particles </span> $\rightarrow$ Isotherms $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Isotherms </primary> <hr> <main> <div style='float: left; width:50%; text-align:left; font-size:30px;'> - Temperature count. - P as a function of volume - No amount of pressure can liquidy a gas. </div> <div style='float: right; width:40%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/8931d7d6-780f-4578-fd86-323526640700/public" width="80%" > <!----> </div> </main> <hr> <footer style = "font-size: 18px">Identical Particles $\rightarrow$ Identical Particles $\rightarrow$ <span style = "color:blue"> Isotherms </span> $\rightarrow$ Thank You $\rightarrow$ </footer>

### <Success style="font-size:25px"> Mean Freepath And Non Ideal Gas L-3 </Success> ### <primary style="font-size:24px"> Thank You </primary> <hr> <main> <div style='float: left; width:100%; text-align:left; font-size:30px;'> </div> <div style='float: right; width:0%;'>  </div> </main> <hr> <footer style = "font-size: 18px">Identical Particles $\rightarrow$ Isotherms $\rightarrow$ <span style = "color:blue"> Thank You </span> $\rightarrow$ $\rightarrow$ </footer>