Chemistry - Ideal Gas Question with Solution | TestHub

(A) At cons. T and n

$$\mathrm{PV}=\text{ const. };\text{ Let }\frac{1}{{\mathrm{V}}^2}=\mathrm{y}\&\mathrm{p}=\mathrm{x}$$

$$\therefore x\times \frac{1}{\sqrt{y}}=\text{ const. or }y=\text{ const }\times x^2$$

(B) Let $V=y;\frac{1}{T}=x$

$$\frac{\mathrm{V}}{\mathrm{T}}=\mathrm{k}(\text{ const. }\mathrm{P},\mathrm{n})\therefore \mathrm{y}\times \mathrm{x}=\mathrm{k}$$

(C) $\log \mathrm{P}=\mathrm{y},\log \mathrm{V}=\mathrm{x}$

$$\begin{array}{rlr}& \mathrm{PV}=\text{ const }(\text{ const. }\mathrm{T},\mathrm{n})& \log \mathrm{P}+\log \mathrm{V}=\log \mathrm{k}\end{array}$$

(D) $V=y,\frac{1}{P^2}=x$

PV = const. (const T & n)

$$\frac{1}{\sqrt{x}}\cdot y=\text{ const. }\Rightarrow y^2=kx$$