Work & Equilibrium of Insulated Box: Why W=0?

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In summary, two equal chambers of air at 400K and different pressures were separated by a frictionless piston and allowed to reach equilibrium. The solution assumes that no work is done on the system, as it is isolated and experiences no external forces or heat.
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princejan7
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Homework Statement



"An insulated box is initially divided by a frictionless, thermally conducting piston. One side of the piston is 1.5(m^3) of air at 400k, 4bar. The other side is 1.5(m^3) of air at 400K,2 bar
The piston is released and equilibrium is attained, with the piston experiencing no change of state"


the solution assumes W=0. why is this?

Homework Equations





The Attempt at a Solution

 
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  • #2
What solution? You didn't post any solution.
 
  • #3
dauto said:
What solution? You didn't post any solution.

here
 

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  • #4
That's the work for the entire system, not the work between the two chambers. Since the entire system is in a isolated box, there is no external work or heat.
 
  • #5


As a scientist, it is important to understand the concept of work and equilibrium in thermodynamics. In this scenario, the insulated box is initially divided by a frictionless, thermally conducting piston. This means that there is no external force acting on the piston and the system is isolated from its surroundings. Therefore, the total work done on the system is equal to zero, since there is no change in the system's internal energy.

In thermodynamics, work is defined as the transfer of energy from one system to another due to a force acting on an object and causing it to move. In this case, since the piston is not moving and there is no external force acting on it, no work is being done on the system.

Furthermore, since the system is in equilibrium, all the forces acting on the system must be balanced. This includes the pressure exerted by the gases on either side of the piston. Since the pressure on both sides is the same, there is no net force acting on the piston and it remains at rest. This is why the solution assumes that W=0, as there is no work being done on the system due to the balanced forces and no change in the system's internal energy.

In conclusion, the assumption that W=0 is based on the understanding of work and equilibrium in thermodynamics. It is important to consider these concepts when analyzing the behavior of a system in order to accurately describe and predict its state.
 

FAQ: Work & Equilibrium of Insulated Box: Why W=0?

What is the concept of work and equilibrium in an insulated box?

Work refers to the application of force on an object to cause a displacement. In the case of an insulated box, equilibrium is achieved when there is no net change in the box's internal energy, meaning the amount of energy entering and leaving the box is equal. This results in a net work of zero, or W=0.

Why is the concept of W=0 important in an insulated box?

In an insulated box, the energy cannot escape or enter the system, so the internal energy must remain constant. This means that any work done on the system must be counteracted by an equal amount of work done by the system. Therefore, the concept of W=0 is important in understanding the balance of energy in an insulated box.

How does the insulation of the box affect the work and equilibrium?

The insulation of the box prevents any heat transfer, which means that the internal energy of the system remains constant. This results in W=0 because there is no change in the internal energy, and thus no net work is done on the system.

Can the work be non-zero in an insulated box?

No, the work must be zero in an insulated box. This is because any work done on the system must be counteracted by an equal amount of work done by the system, resulting in a net work of zero. If the work were non-zero, it would mean that the internal energy of the system is changing, which is not possible in an insulated box.

How does the concept of W=0 apply to other isolated systems?

The concept of W=0 applies to any isolated system where there is no exchange of energy with the surroundings. This includes systems such as a closed container with no openings or a planet in orbit around the sun. In all these cases, the internal energy remains constant, resulting in W=0.

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