Temperature Limits in Heat Conducting Piston Problem with Friction

• grassstrip1
In summary, the conversation discusses a problem where air in an insulated cylinder is separated by a piston into two equal valves. The system comes to a new equilibrium position after the pin is removed, with equal pressures in both chambers. The piston is heat conducting and there is friction between the piston and cylinder walls, but this does not affect the mechanical equilibrium condition. The task is to estimate the upper and lower limits for the temperature in chambers A and B, given the initial temperatures and pressures. The problem is not adiabatic and the temperature may differ between the two chambers due to the partition not being heat conducting. More information is needed to solve the problem completely.
grassstrip1

Homework Statement

Air in an insulated cylinder is separated by a piston into two equal valves. When the pin is
removed, the system comes to a new equilibrium position. There is friction between the piston and
the cylinder walls but friction does not influence the mechanical equilibrium condition (at the final
state, the pressures are equal). For case (1) the piston
is heat conducting.
Estimate the upper and
lower limits for the temperature in chamber A and B

For Chamber A given: T1=300k, P1= 2bar
For Chamber B given: T1=300k P1=1bar
**Picture attatched**

pv=nRt

The Attempt at a Solution

Considering one side at a time this doesn't seem like a constant volume, pressure or adiabatic problem.
From pv=nRt the amount of moles in Chamber A are twice that in chamber B.
-Given that the piston is heat conducting does this mean that the temperature will be the same for chamber A and B at equilibrium, why would there be two different temperature limits? Even then, it feels like there's missing information to solve the problem, PVϒ = Constant doesn't apply here I don't think since the process is not adiabatic

Attachments

• therm.JPG
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Term adiabatic is for process. This process is not adiabatic as you guess correctly. Piston is conducting and friction exists between piston and cylinder walls does not make it isothermal also. Internal energy is not conserved. Pressure becomes same at equilibrium but the temperature which is the measure of average internal energy per molecule could be different in two chambers as the partition is perhaps not conducting. At present I can say only this much.

1. What is the first law of thermodynamics?

The first law of thermodynamics, also known as the law of conservation of energy, states that energy can neither be created nor destroyed, but can only be transferred or converted from one form to another.

2. How does the first law of thermodynamics apply to piston problems?

In piston problems, the first law of thermodynamics is used to analyze the changes in energy, work, and heat transfer of a system involving a moving piston. It helps determine the relationship between the changes in internal energy and the work done by the system.

3. What is the formula for calculating work in a piston problem?

The formula for calculating work in a piston problem is W = PΔV, where W is the work done, P is the pressure, and ΔV is the change in volume of the system.

4. How does the first law of thermodynamics relate to the ideal gas law?

The ideal gas law, which states that the pressure, volume, and temperature of an ideal gas are all interrelated, is derived from the first law of thermodynamics. This is because the first law states that the change in internal energy of a system is equal to the work done on the system plus the heat transferred to the system, and in an ideal gas, the internal energy is solely dependent on the temperature.

5. Can the first law of thermodynamics be violated in a piston problem?

No, the first law of thermodynamics is a fundamental law of nature and cannot be violated in any physical process, including piston problems. This means that the total energy of the system must remain constant, and any changes in energy must be accounted for by work done or heat transferred.

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