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Pressure

An ideal gas ...

Question

An ideal gas is filled in a cylinder, which is fitted with a movable non-conducting piston as shown in the figure. The gas in the cylinder is heated slowly. The gas expands and pistons moves towards right. If the temperature of the gas is increased slowly from $T_{0}$ to $2 T_{0}$ , find the displacement of the piston. (Given atmospheric pressure = $P_{0}$ and area of cross-section of the cylinder = $A$ ).

A

\frac{V_{0}}{2 A}

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B

\frac{5 V_{0}}{2 A}

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C

\frac{2 V_{0}}{3 A}

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D

\frac{V_{0}}{A}

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Solution

The correct option is D $\frac{V_{0}}{A}$
Initially

$P A = P_{0} A ⟹ P = P_{0}$

Finally
$P_{f} = P_{0}$

volume inceases as pressure remains constant in this process.

$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$

$\frac{V_{0}}{T_{0}} = \frac{V_{0} + A x}{2 T_{0}}$

$V_{0} = \frac{V_{0} + A x}{2}$

$2 V_{0} = V_{0} + A x$

$⟹ x = \frac{V_{0}}{A}$

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