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A glass tube scaled at both ends is $1 \mathrm{~m}$ long. It lies horizontally with the middle $10 \mathrm{~cm}$ containing $\mathrm{Hg}$ . The two ends of the tube, eqaul in length, contain air at $27^{\circ} \mathrm{C}$ and pressure $76 \mathrm{~cm}$ of $\mathrm{Hg}$ . The temperature at one end is kept $0^{\circ} \mathrm{C}$ and at the other end it $127^{\circ} \mathrm{C}$ . Neglect the change in length of $\mathrm{Hg}$ column. Then the change in length on two sides is
Option: 1
$12.3 \mathrm{~cm}$

Option: 2
$10.311 \mathrm{~cm}$

Option: 3
$9.9 \mathrm{~cm}$

Option: 4
$8.49 \mathrm{~cm}$

Answers (1)

best_answer

Initially $l=45 \mathrm{~cm}(2 l+10=100 \mathrm{~cm})$

$\mathrm{P}_{1}=\mathrm{P}_{2}=\mathrm{P} \text { (say) }\quad \ldots(i)$
(a)

(b)

Applying gas law at end $\mathrm{A}$ ,

$\frac{45 \mathrm{AP}}{300}=\frac{(45-\mathrm{x}) \mathrm{AP}_{1}}{273}\quad \ldots(ii)$
$\text{At end}\: \mathrm{B} \: \frac{45 \mathrm{AP}}{300}=\frac{(45+\mathrm{x}) \mathrm{AP}_{2}}{400}\quad \ldots(iii)$

From (i), (ii) and (iii)
$\frac{(45-\mathrm{x})}{273}=\frac{45+\mathrm{x}}{400}=8.49 \mathrm{~cm}$

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