A closed hollow insulated cylinder is filled with gas at 0^ ^ ^ C...

A closed hollow insulated cylinder is filled with gas at

0^{{}^{{}^{\circ}}} \mathrm{C}

and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas in one side of the piston is heated to

100^{{}^{{}^{\circ}}} \mathrm{C}

. If the piston moves

5 \mathrm{~cm}

. The length of the hollow cylinder is

Options

A $15.65 \mathrm{~cm}$
B $27.3 \mathrm{~cm}$
C $38.6 \mathrm{~cm}$
D $64.6 \mathrm{~cm}$

Correct answer

D. $64.6 \mathrm{~cm}$

Step-by-step solution

From Charle's law,

\frac{V_1}{V_2}=\frac{T_1}{T_2}

Volume

(V)

is proportional to the length of hollow cylinder.

\begin{aligned} \frac{l_1}{l_2} & =\frac{T_1}{T_2} \\ \frac{l+5}{l-5} & =\frac{273+100}{273+0} \\ \frac{l+5}{l-5} & =\frac{373}{273} \\ \frac{2 l}{10} & =\frac{646}{100} \\ & =\frac{646 \times 10}{2 \times 100}=32.3 \mathrm{~cm}\end{aligned}

\begin{aligned} \therefore \text { Length of cylinder } & =2 l=2 \times 32.3 \\ & =64.6 \mathrm{~cm}\end{aligned}

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