NEET Practice Questions (MCQs) with Answers & Solutions

the temperature above which a substance can exist only in gaseous state

$$\begin{gathered} \frac{T_C}{P_C}=\frac{8a\times 27b^2}{27Rb\times a}=\frac{8b}{R} \\ {V}_{Excluded}=nb \end{gathered}$$

3.

Critical Temperature: The temperature which above, a substance can not exist as a liquid, no matter how much pressure is applied. Every substance has a critical temperature.

3.

temperature for which the second virial coefficient, becomes 0. It is at this temperature that the attractive forces and the repulsive forces acting on the gas particles balance out.

It is the temperature at which gas shows neither cooling effect nor heating effect i.e., Joule-Thomson coefficient µ = 1. Below this temperature, it shows cooling effect and above this temperature, it shows heating effect.

Any gas like H₂, H­_e etc, whose inversion temperature is low would show heating effect at room temperature. However, if these gases are just cooled below inversion temperature and then subjected to Joule-Thomson effect, they will also undergo cooling.

$$\begin{gathered} \mathrm{The} \mathrm{van} \mathrm{der} \mathrm{Waal}\text{'}\mathrm{s} \mathrm{equation} \mathrm{for} 1 \mathrm{mole} \mathrm{of} \mathrm{gas} \mathrm{is} \\ \left(\mathrm{P}+\frac{\mathrm{a}}{{\mathrm{V}}^2}\right) \left(\mathrm{V}-\mathrm{b}\right)=\mathrm{RT} \\ \mathrm{if} \mathrm{we} \mathrm{put}, {\mathrm{P}}_{\mathrm{r}}=\frac{\mathrm{P}}{{\mathrm{P}}_{\mathrm{C}}}, {\mathrm{V}}_{\mathrm{r}}=\frac{{\mathrm{V}}_{\mathrm{m}}}{{\mathrm{V}}_{\mathrm{c}}} \mathrm{and} {\mathrm{T}}_{\mathrm{r}}=\frac{\mathrm{T}}{{\mathrm{T}}_{\mathrm{C}}}; \\ \left(\because {\mathrm{P}}_{\mathrm{C}}=\frac{\mathrm{a}}{27 {\mathrm{b}}^2}, {\mathrm{V}}_{\mathrm{C}}=3\mathrm{b} \mathrm{and} {\mathrm{T}}_{\mathrm{C}}=\frac{8\mathrm{a}}{27 \mathrm{Rb}}\right) \\ \left({\mathrm{P}}_{\mathrm{r}}\left(\frac{{\mathrm{a}}^2}{27 {\mathrm{b}}^2}\right)+\frac{\mathrm{a}}{{\mathrm{V}}_{\mathrm{r}}^2{\left(3\mathrm{b}\right)}^2}\right) \left({\mathrm{V}}_{\mathrm{r}}\left(3\mathrm{b}\right)-\mathrm{b}\right)={\mathrm{RT}}_{\mathrm{r}} \left(\frac{8\mathrm{a}}{27\mathrm{Rb}}\right) \\ \mathrm{This} \mathrm{equation} \mathrm{is} \mathrm{called} \mathrm{van} \mathrm{der} \mathrm{Waal}\text{'}\mathrm{s} \mathrm{equation} \mathrm{of} \mathrm{law} \mathrm{of} \mathrm{corresponding} \mathrm{states}. \end{gathered}$$

(b) This is the derived formula for W_rev in adiabatic process.