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An insulated cylindrical vessel open at one end is fitted with an insulated piston of negligible weight and negligible thickness at the mid point of the vessel. The cylinder contains a gas at $0^{\circ} C .$ When the gas is heated to $100^{\circ} C,$ the piston moves through a length of 5cm. Length of the cylindrical vessel in cm is

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13. 65

27.3

38.6

64.6

answer is B.

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Detailed Solution

Given that,

Initial temperature, $t_{1} = 0^{0} C$

Final temperature, $t_{2} = 100 º C$

Moving length of piston = 5 cm

The above given process is isobaric

$V_{1} / T_{1} = V_{2} {/T}_{2}$

$\begin{array}{l} (L/2) / 273 = ((L / 2) + 5) / 373, \\ L / 546 = L + 10 / 746 \end{array}$

$L = 27 . 3cm$

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