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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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Rishi

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