Find the tension in the wire - Heat and thermodynamics

AI Thread Summary
The discussion centers on calculating the tension in a wire connecting two pistons in a horizontal cylindrical tube as the temperature of the gas increases from To to 3To. Initially, the pressure is equal to atmospheric pressure, Po. When the temperature rises, the pressure inside the tube increases to 3Po, but the volume remains constant. A force balance on one piston reveals that the tension in the wire is actually 2PoA, accounting for both the internal pressure and atmospheric pressure acting on the pistons. The calculation clarifies the relationship between temperature, pressure, and tension in the system.
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consider a horizontal cylindrical tube of cross sectional area A fitted with two frictionless pistons. The piston are connected to each other by an inextensible wire. Initially, the temperature of the gas is To and its pressure is Po which equals the atmospheric pressure. Find the tension in the wire if the temperature is raised to 3To.

my attempt..
since the pressure is constant..
what i tried to do was assume the volume to be constant..
so if the volume was constant, pressure developed would be..
(P1)V = nRTo
(P2)(V) = nR(3To)
or, P2 = 3P1
so, the force on each cross section = (3Po.A)
so this must be the tension in the wire..
but the answer says its (2Po.A).. which definitely needs to be correct..
so where m i wrong? please suggest.
Thanks in advance..!
 
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exuberant.me said:
its pressure is Po which equals the atmospheric pressure.
What about the atmosphere?
 
The standard atmosphere (symbol: atm) is a unit of pressure equal to 101.325 kPa
 
I mean: how does the atmosphere affect the tension?
 
Do a force balance on one of the pistons and see what you get. The forces acting on the piston are the pressure force on the inside face of the piston, the pressure force of the atmosphere on the outside face of the piston, and the wire tension.
 
P'A = PoA + T

Now when the temperature of the system is increased to 3To and if we assume the volume to be constant..
pressure developed,
PoV = nRTo and P'V = nR(3To)
=> P' = 3PoA

thus, T = 3PoA - PoA = 2PoA

@Chestermiller - Thanks a lot sir..!
 

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