Work Done Compressing a Gas

[Ghost Repeater]

Homework Statement

This is a conceptual question.

An ideal gas is compressed to half its initial volume by means of several possible processes. Which of the following processes results in the most work done on the gas? a) isothermal b) adiabatic c) isobaric d) The work done is independent of the process.

2. Homework Equations

I'm deliberately trying to avoid using equations. I'm trying to reason it out 'physically' rather than 'algebraically' using formulas.

The Attempt at a Solution

[/B]
As I said, I'm trying to reason this through physically, by imagining what happens to the gas molecules and their energy as the volume decreases. So far, what I have is this.

More work will be required in compressing the gas adiabatically than isothermally. The reason for this is that, as you press on the gas to reduce its volume, you increase its energy by doing work on it. In an isothermal process, this energy is not allowed to increase the gas's temperature. It will be 'sapped out' of the gas by a cold bath reservoir or something of that nature. In an adiabatic process, however, the energy you transfer to the gas by doing work on it (compressing it) has no way of leaving the container, so it stays there and makes the molecules more energetic (i.e. raises temperature), which means you have to do more work still to compress the gas down further.

Is this a correct intuition about the adiabatic versus isothermal case?

As for the adiabatic vs isobaric case, as you compress the gas, in order for the pressure to stay the same, the temperature has to drop. This means the internal energy has to drop. Whereas in the adiabatic case, the internal energy had to increase. Does this mean the adiabatic case requires more work, since the molecules have more energy with which to 'resist' the compression?

 

[Chestermiller]

Homework Statement

This is a conceptual question.

An ideal gas is compressed to half its initial volume by means of several possible processes. Which of the following processes results in the most work done on the gas? a) isothermal b) adiabatic c) isobaric d) The work done is independent of the process.

2. Homework Equations

I'm deliberately trying to avoid using equations. I'm trying to reason it out 'physically' rather than 'algebraically' using formulas.

The Attempt at a Solution

[/B]
As I said, I'm trying to reason this through physically, by imagining what happens to the gas molecules and their energy as the volume decreases. So far, what I have is this.

More work will be required in compressing the gas adiabatically than isothermally. The reason for this is that, as you press on the gas to reduce its volume, you increase its energy by doing work on it. In an isothermal process, this energy is not allowed to increase the gas's temperature. It will be 'sapped out' of the gas by a cold bath reservoir or something of that nature. In an adiabatic process, however, the energy you transfer to the gas by doing work on it (compressing it) has no way of leaving the container, so it stays there and makes the molecules more energetic (i.e. raises temperature), which means you have to do more work still to compress the gas down further.

Is this a correct intuition about the adiabatic versus isothermal case?

As for the adiabatic vs isobaric case, as you compress the gas, in order for the pressure to stay the same, the temperature has to drop. This means the internal energy has to drop. Whereas in the adiabatic case, the internal energy had to increase. Does this mean the adiabatic case requires more work, since the molecules have more energy with which to 'resist' the compression?

Yes and yes. Now, compare isothermal with isobaric.