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Byju's Answer

Standard XII

Physics

Pressure vs Velocity

An open cylin...

Question

An open cylindrical tube of cross-sectional area $A$ has two air tight frictionless pistons at its two ends. The pistons are tied with a straight piece of metallic wire. The tube contains a gas at atmospheric pressure $P_{0}$ and temperature $T_{0}$ in between the pistons. If temperature of the gas is doubled, then the tension in the wire is
(Assume that metallic wire is rigid)

4 P_{0} A

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\frac{P_{0} A}{2}

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P_{0} A

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2 P_{0} A

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Solution

The correct option is C $P_{0} A$
As the metallic wire is rigid, volume of gas between the piston remains constant. Given that on increasing temperature, pressure becomes double.
$V =$ constant.
$T =$ doubled
$P = 2 P_{0}$

FBD of piston is
For equilibrium
$P_{0} A + T_{0} = 2 P_{0} A$
$T_{0} = P_{0} A$

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The correct option is C P0AAs the metallic wire is rigid, volume of gas between the piston remains constant. Given that on increasing temperature, pressure becomes double. V= constant. T= doubled P=2P0 FBD of piston is For equilibrium P0A+T0=2P0A T0=P0A