Find the tension in the wire - Heat and thermodynamics

In summary, the conversation discusses a horizontal cylindrical tube with two frictionless pistons connected by an inextensible wire. Initially, the temperature of the gas inside is To and the pressure is equal to atmospheric pressure. When the temperature is raised to 3To, the tension in the wire can be found by considering the forces acting on the piston, which include the pressure force from the atmosphere and the wire tension. By assuming constant volume, the tension is calculated to be 2 times the atmospheric pressure multiplied by the cross sectional area of the tube.
  • #1
exuberant.me
29
1
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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  • #2
exuberant.me said:
its pressure is Po which equals the atmospheric pressure.
What about the atmosphere?
 
  • #3
The standard atmosphere (symbol: atm) is a unit of pressure equal to 101.325 kPa
 
  • #4
I mean: how does the atmosphere affect the tension?
 
  • #5
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.
 
  • #6
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..!
 

FAQ: Find the tension in the wire - Heat and thermodynamics

What is tension in a wire and how does it relate to heat and thermodynamics?

Tension in a wire refers to the amount of force acting on the wire in order to keep it taut. In the context of heat and thermodynamics, tension can affect the thermal expansion of the wire and ultimately impact its temperature and conductivity.

How do you calculate the tension in a wire?

The tension in a wire can be calculated using the formula T = F * L, where T is tension, F is the force applied to the wire, and L is the length of the wire.

What factors can affect the tension in a wire?

The tension in a wire can be affected by various factors such as the material and diameter of the wire, the temperature and thermal expansion of the wire, and the force applied to the wire.

How does tension in a wire impact its thermal conductivity?

Tension can impact the thermal conductivity of a wire by affecting its shape and dimensions, which can in turn affect the flow of heat through the wire. A taut wire may have a higher thermal conductivity than a slack wire, as it allows for more efficient heat transfer.

Why is it important to consider tension in a wire when studying heat and thermodynamics?

Tension in a wire can have a significant impact on its thermal properties, such as its conductivity and expansion. Understanding and controlling the tension in a wire is important in order to accurately study and predict the behavior of heat and thermodynamics in various systems and applications.

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