Question

A vertical hollow cylinder of height $152$cm is fitted with a weightless piston. The lower half is filled with an ideal gas and the upper half with mercury. The cylinder is now heated at $300$K, so that $\frac{1}{4}$ th of the mercury comes out. Find the temperature at which it will happen assuming thermal expansion of Hg to be negligible?

• A. $340$ K
• B. $330.6$ K
• C. $328.12$ K
• D. $322.2$ K

Answer 1

Answer: (C)

$328.12$ K

Solution:- (C) $328.12K$

Let $x$ be that volume of the cylinder.

Initially at lower end-

$P=76\text{cm of Hg}+76\text{cm of air}=152cm$

$T=300K$

$V=\frac{x}{2}$

Finally at lower end-

$P=57\text{cm of Hg}+76\text{cm of air}=133cm$

$T=?$

$V=\frac{5x}{8}$

Therefore, for an ideal gas

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

$\frac{152\times \frac{x}{2}}{300}=\frac{133\times \frac{5}{8}x}{T}$

$\Rightarrow T=\frac{133\times 5\times 2\times 300}{152\times 8}$

$\Rightarrow T=328.12K$