# Work done by a gas in a piston

#### goggles31

Let's assume that weights are placed on a massless piston and below the piston is a gas. If we remove all the weights at once, the work done by the gas should be the difference between the forces exerted by the gas and the atmosphere multiplied by the change in volume. However, we know that the pressure exerted by a gas is inversely proportional to its volume and hence the work done is given by the area under a curve. Is it okay to assume that the pressure of the gas instantaneously changes to atmospheric pressure when the weights are removed, as in Figure 4.10 of the link given?

http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node34.html

Related Other Physics Topics News on Phys.org

#### BiGyElLoWhAt

Gold Member
I don't think that seems very reasonable. Try solving $PV^{\gamma}=nRT$

#### Chestermiller

Mentor
Let's assume that weights are placed on a massless piston and below the piston is a gas. If we remove all the weights at once, the work done by the gas should be the difference between the forces exerted by the gas and the atmosphere multiplied by the change in volume. However, we know that the pressure exerted by a gas is inversely proportional to its volume and hence the work done is given by the area under a curve. Is it okay to assume that the pressure of the gas instantaneously changes to atmospheric pressure when the weights are removed, as in Figure 4.10 of the link given?

http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node34.html
In an irreversible expansion, the pressure exerted by a gas on the piston is not inversely proportional to its volume. The gas pressure is not even uniform spatially within the cylinder during an irreversible expansion. Plus, the force is affected by viscous (dissipative) stresses in the gas such that the rate of change of volume also affects the force. However, the work that the gas does on the piston can be determined if we know the external force applied to the gas at the piston face (because the gas pressure matches the "external pressure" at the piston face).

For more details on this, see my two Physics Forums Insights articles: https://www.physicsforums.com/insights/understanding-entropy-2nd-law-thermodynamics/ and https://www.physicsforums.com/insights/reversible-vs-irreversible-gas-compressionexpansion-work/

#### Chestermiller

Mentor
I don't think that seems very reasonable. Try solving $PV^{\gamma}=nRT$
This equation is not valid for an irreversible expansion, or any other expansion for that matter. If the expansion is reversible, then the ideal gas law applies (exactly as it is always written).

#### BiGyElLoWhAt

Gold Member
Also, in the link, the processes are explicitly reversible.

#### Chestermiller

Mentor
Also, in the link, the processes are explicitly reversible.
Not for the cases where finite weights are suddenly removed from the piston.

Mentor

#### BiGyElLoWhAt

Gold Member
Hmm... I see. Removing each small weight is what they're referring to as reversible. Sorry about that.

#### Chestermiller

Mentor
Hmm... I see. Removing each small weight is what they're referring to as reversible. Sorry about that.
No problem. These things are always very confusing.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving