First slide

laws

Question

A cylindrical tube of uniform cross-sectional area A is fitted with two air tight frictionless pistons.
The pistons are connected to each other by a metallic wire. Initially, the pressure of the gas is p₀and temperature is T₀, atmospheric pressure is also p₀. Now, the temperature of the gas is increased to 2T₀, the tension in the wire will be

Moderate

A

2p₀A
B

p₀A
C

$\frac{p_{0} A}{2}$
D

4p₀A

Solution

Volume of the gas V is constant.
$∴ p \propto T,$ i.e. pressure will be doubled when temperature is doubled.
$∴$ p = 2p₀
Now, let F be the tension in the wire. Then, equilibrium of anyone piston will give
$F = (p - p_{0}) A$
$= (2 p_{0} - p_{0}) A$
= p₀A

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