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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
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The correct answer is:
$190 \mathrm{cc}$
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
$p_i V_i=p_f V_f$
$\begin{array}{ll}\Rightarrow 760 \times 100=400 \times V_f \\ \Rightarrow \quad & V_f=\frac{760 \times 100}{400}\end{array}$
$=190 \mathrm{~cm}^3=190 \mathrm{cc} \quad\left[\because \mathrm{lcm}^3=1 \mathrm{cc}\right]$
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
$p_i V_i=p_f V_f$
$\begin{array}{ll}\Rightarrow 760 \times 100=400 \times V_f \\ \Rightarrow \quad & V_f=\frac{760 \times 100}{400}\end{array}$
$=190 \mathrm{~cm}^3=190 \mathrm{cc} \quad\left[\because \mathrm{lcm}^3=1 \mathrm{cc}\right]$
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