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Question
Figure shows a cylindrical tube of cross-sectional area A fitted with two frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the temperature of the gas is T0 and its pressure is p0 which equals the atmospheric pressure. (a) What is the tension in the wire? (b) What will be the tension if the temperature is increased to 2T0 ?
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Solution
(a)
Since pressure from outside and inside the cylinder is the same, there is no net pressure acting on the pistons. So, tension will be zero.
(b)
`T_1 = T_0`
`T_2 = 2T_0`
`P_1 = P_0 = 10^5 "Pa"`
CSA = A
Let the Pistons be L distance apart .
V = AL
Applying five variable gas equation , we get
`(P_1V)/T_1 = (P_2V)/T_2`
⇒ `10^5/T_0 = P_2/(2T_0)`
⇒ `P_2 = 2×10^5 = 2P_0`
Net Force acting outside = `2P_0 - P_0 = P_0`
Force acting on a piston `F = P_0A`
By the free body diagram , we get
`F - T = 0`
`T = P_0A`
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