# Tension in the Wire- Thermodynamics Question

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1. Jan 13, 2015

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
(P1V1)/T1=(P2V2)/T2

3. The attempt at a solution
Using the above equation; as volume is constant, new pressure P'=3Po. So, force applied on one piston=3PoA

Equating with the force from atmospheric pressure outside the tube,
3PoA=PoA+T
So T=2PoA ; which is the required answer.

My question is, isn't this the force on one cross section of the wire? So why isn't this answer multiplied by two?

Thank you for your time!

2. Jan 13, 2015

### haruspex

It's a common mistake to think that if there's a pull F on each end of the wire then the tension must be 2F.
You need to understand how tension is defined. If we say that the tension is T at some point in a wire (need not be the same all along the wire) we mean that if you were to insert a block at that point in the wire the block would experience a pull T on each side. Thus, if the tension is the same all the way along then it is also equal to the force exerted at each end.
Is that your question?

3. Jan 14, 2015

Yes, thank you very much! So if there /is/ such a wire which is experiencing a force F on both sides, and assuming it experiences equal tension everywhere; the tension would be F?

4. Jan 14, 2015

### haruspex

Yes.

5. Jan 14, 2015

And if one end of this wire was fixed to a wall and force F was applied on the free end, it would still experience the same tension F as in the earlier case because of reaction force from the wall?

6. Jan 14, 2015

### Staff: Mentor

Yes.

7. Jan 15, 2015