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 P 0 and temperature is T 0 , atmospheric pressure is also P 0 . Now the temperature of the gas is increased to 2T 0 , the tension in the wire will be
$(a) 2P_{0}A (b) P_{0}A (c) \frac{P_{0}A}{2} (d) 4P_{0}A$
Text Solution
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Volume of the gas is constant V = constant ∴ ∴ $\mathrm{P} \propto \mathrm{T}$
i.e., pressure will be doubled if temperature is doubled
∴ ∴ $P = 2P_0$
Now let F be the tension in the wire. Then equilibrium of any one piston gives
$\mathbf{F} = (P - P_0) A = (2P_0 - P_0) A = P_0 A$
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