The volume of a gas at $30^{\circ} \mathrm{C}$ temperature and $760 \mathrm{~mm}$ of $\mathrm{Hg}$ pressure…

The volume of a gas at $30^{\circ} \mathrm{C}$ temperature and $760 \mathrm{~mm}$ of $\mathrm{Hg}$ pressure is $100 \mathrm{cc}$. Then its volume at the same temperature and $400 \mathrm{~mm}$ of $\mathrm{Hg}$ is
  1. $190 \mathrm{cc}$
  2. $210 \mathrm{cc}$
  3. $150 \mathrm{cc}$
  4. 120 cc

Solution

Given, initial volume $=100 \mathrm{~cm}^3$ Initial pressure $=760 \mathrm{~mm}$ of $\mathrm{Hg}$ Initial temperature $=30^{\circ} \mathrm{C}$ And, final temperature $=$ Initial temperature So, change is isothermal. Also final pressure $=400 \mathrm{~mm}$ of $\mathrm{Hg}$ Now, for an isothermal change $p_i V_i=p_f V_f$ $\begin{array}{ll}\Rightarrow 760 \times 100=400 \times V_f \\ \Rightarrow \quad & V_f=\frac{760 \times 100}{400}\end{array}$ $=190 \mathrm{~cm}^3=190 \mathrm{cc} \quad\left[\because \mathrm{lcm}^3=1 \mathrm{cc}\right]$

Asked in: AP EAMCET 2022 (07 Jul Shift 1)

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