A horizontal uniform glass tube of 100 ,cm, length sealed at both… - Vidyadip

MCQ

A horizontal uniform glass tube of $100 \,cm$, length sealed at both ends contain $10 \,cm$ mercury column in the middle. The temperature and pressure of air on either side of mercury column are respectively $81°C$ and $76\, cm$ of mercury. If the air column at one end is kept at $0°C$ and the other end at $273°C$, the pressure of air which is at $0°C$ is (in $cm$ of $Hg$)

A
$76$
B
$68.2$
✓
$102.4$
D
$122$

✓

Answer

Correct option: C.

$102.4$

c
Let $x$ be the displacement of the mercury column on the side whose temperature is changed to $0^{\circ} C$. New pressure on both sides must be same so that the mercury column remains in equilibrium.

$\frac{ PV }{ T }$ is constant for air column.

$\Rightarrow \frac{P_{0}(45)}{273+31}=\frac{P_{1}(45-x)}{273+0}$

and $\frac{P_{0}(45)}{273+31}=\frac{P_{1}(45+x)}{273+273}$

Therefore, $x =15 \; cm$ and thus $P =102.4 \; cm$ of $Hg$

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