Stationary vertical cylinder with heavy piston

[BobaJ]

Hi,

I'm just starting to learn thermodynamics and I'm completely stuck with a problem:

1. Homework Statement

A stationary vertical cylinder, closed at the top, contains a gas whose volume may be changed with the aid of a heavy, frictionless piston of weight w.

a) How much work is done by the external force in compressing the gas by an amount dV by raising the piston a distance dy?
b) If this device is used as part of an engine, what expression is appropriate to calculate the net work delivered to or received from the surroundings?
c) If this device is used only to produce temperature changes of the gas, what expression for work would be appropriate?

Homework Equations

The Attempt at a Solution

Ok, if I'm not wrong that would be classified as a typical hydrostatic system with thermodynamic coordinates P, V and T. And it should be a quasi-static process. Can I assume that the gas is an ideal gas and that the process would be isothermal? So that $$ W=-\int_{V_{i}}^{V_{f}} P dV $$?
Then, by getting a free body diagram, I could work out an equation for P? But I'm stuck on the fbd.

For question b, I assume that it would have to be the net work done during a cycle. Which would be the combination of compression and expansion.

And for question c, I think it should be an isobaric process? So that the Volume and the temperature change but the pressure stays constant?

Are these assumptions and ideas correct and how could I formalize them to answer the questions properly?

Thanks a lot!

 

[Chestermiller]

Hi,

I'm just starting to learn thermodynamics and I'm completely stuck with a problem:

1. Homework Statement

A stationary vertical cylinder, closed at the top, contains a gas whose volume may be changed with the aid of a heavy, frictionless piston of weight w.

a) How much work is done by the external force in compressing the gas by an amount dV by raising the piston a distance dy?
b) If this device is used as part of an engine, what expression is appropriate to calculate the net work delivered to or received from the surroundings?
c) If this device is used only to produce temperature changes of the gas, what expression for work would be appropriate?

Homework Equations

The Attempt at a Solution

Ok, if I'm not wrong that would be classified as a typical hydrostatic system with thermodynamic coordinates P, V and T. And it should be a quasi-static process. Can I assume that the gas is an ideal gas and that the process would be isothermal? So that $$ W=-\int_{V_{i}}^{V_{f}} P dV $$?
Then, by getting a free body diagram, I could work out an equation for P? But I'm stuck on the fbd.

For question b, I assume that it would have to be the net work done during a cycle. Which would be the combination of compression and expansion.

And for question c, I think it should be an isobaric process? So that the Volume and the temperature change but the pressure stays constant?

Are these assumptions and ideas correct and how could I formalize them to answer the questions properly?

Thanks a lot!

The reason you are struggling so much with this is that the problem statement is not very clear or precise. In part (a), if it is quasi static, and you do a force balance on the piston, what does that tell you about PdV and wdy?

I have no idea what they are talking about in (b) and (c)

 

[BobaJ]

Yes, I know. The instructions here are very unclear. I have the feeling that they leaf out a lot of important information.

Well. The gas is exerting a hydrostatic pressure on its surroundings. As the piston is at the bottom of the cylinder. This pressure would the whole weight of the gas per Area. If I push the piston a distance dy inside the cylinder, the volume should decrease by dV. So, PdV should be a negative quantity. So, the work would be positive and that obviously means, that the work is done on the system. As I understand it, it doesn't matter where the external force is coming from, only that it exists. But I don't know how to formalize all this.

 

[Chestermiller]

Yes, I know. The instructions here are very unclear. I have the feeling that they leaf out a lot of important information.

Well. The gas is exerting a hydrostatic pressure on its surroundings. As the piston is at the bottom of the cylinder. This pressure would the whole weight of the gas per Area. If I push the piston a distance dy inside the cylinder, the volume should decrease by dV. So, PdV should be a negative quantity. So, the work would be positive and that obviously means, that the work is done on the system. As I understand it, it doesn't matter where the external force is coming from, only that it exists. But I don't know how to formalize all this.

From a free body diagram, what is the force balance on the piston?