PV Diagrams - Thermodynamics - A Generic Thermodynamic Process - How to Find the Amount of Work Done

Oct 25, 2026

PV diagrams and piston-cylinder thermodynamics are used to explain a generic thermodynamic process involving changes in internal energy, temperature, pressure, and volume. The material describes heat transfer and work interactions, focusing on isobaric (constant-pressure) expansion. It derives the work done using pressure and piston displacement, yielding W = PΔV. It also links the sign of work to cyclic processes and states that the enclosed area on a pressure–volume plot corresponds to the work for one cycle.

LanguageEnglish

CategoryTechnology

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Reading Time48 min

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PV Diagrams - Thermodynamics

A Generic Thermodynamic Process

Pistons and Cylinders

Isobaric Process (Constant Pressure)

How to Find the Amount of Work Done

Sign of Work

Work Done Using a P-V Diagram

PV Diagrams THERMODYNAMICS | A Generic Thermodynamic Process
| | | | --- | --- | --- | | Start with some internal energy due to a starting T, P, and V | Internal Energy
U1 T1 P 1 V1

Thermodynamic Process

Q

W
Heat is added or taken away, work is done on or by the gas
Internal Energy
U2 T2 P 2 V2
You end up with an new amount of internal energy, with new T, P, and V | | | Many engines that do work involve pistons and
cylinders.
| | | --- | --- | | 􀁹 A cylinder is tube and a piston is a solid cylindrical device that exactly fits into the cylinder so that thereis very little gap between the piston and the side of the cylinder. | | | | piston
cylinder | | | | | Pistons and Cylinders | | --- | | 􀁹 The piston can move up and down in the cylinder.
􀁹 Inside the cylinder, under the piston, is a gas.
􀁹 The gas cannot escape around the piston.
􀁹 Push down on the piston and the gas is compressed into a smaller volume.
􀁹 Pull up on the piston and the gas expands into a larger volume.
􀁹 The motion of the piston involves work. If you do work on the piston, you make it move. If the gas expands or is compressed causing the piston to move, then work is done on the piston (the gas is doing the work) . | | | | isobaric process: constant P
| | --- | | 􀁹 If you add heat to the cylinder, the gas expands and pushes the piston upwards, doing work on it. We make a major assumption – that the pressure stays constant. This is actually reasonable. The area on the top of the piston doesn’t change, so the force exerted on it by the atmosphere is constant. When the piston rises to some position, the force pushing down is still the same, so the force inside pushing up must be the same as well. Since this force comes from the pressure, the pressure must still be the same.

Gas expands at constant pressure moving piston a distance of 􀀧 y | | isobaric process: constant P
| | | --- | --- | | | 􀁹 What a P-V Diagram would look like
| | | | | How to Find the Amount of Work Done | | --- | | 􀁹 The piston has moved a distance of 􀀧 y.
􀁹 A force pushed the piston upward.
􀁹 Work happens when a force causes an object to move.
􀁹 So can we figure out how much work was done on the piston?
􀁹 Well, we know that pressure is the force divided by the area it acts on: P=F/a
􀁹 The force exerted by the pressure is equal to:
F = PA
􀁹
􀁹 The definition of work is: W=Fd 􀁹
􀁹
􀁹 So, plugging in the value of the force, we get: W 􀀠 Fd 􀀠 􀀋 PA􀀌d 􀀠 PAd 􀁹
􀁹
􀁹 We know that the area of this cylinder multiplied by its height is its change in volume: 􀀧V 􀀠 Ad 􀁹
􀁹
􀁹 Therefore, plugging this in forAd we get: W 􀀠 PAd 􀀠 P 􀀋􀀧V􀀌 􀀠 P􀀧V 􀁹
􀁹 So W 􀀠 P􀀧V 􀁹
􀁹 | | | | Sign of work
| | --- | | | | | | How to Find the Amount of Work Done
| | | | --- | --- | --- | | 􀁹 The area under the curve is equal to the work that is done.
􀁹 This is also true for any graph of pressure vs volume. The area under the curve is always equal to the work.
W 􀀠 P􀀧V | | | | | |
| | | | | | Work Done Using a P-V Diagram | | | --- | --- | | 􀁹 note that in a cyclic process the gas is taken through a cycle of operations and brought back to the original state. If the cycle is clockwise as in the present case, work is done by the gas. So the work is negative. Further, the area enclosed by the closed curve gives the work done during one cycle. | | | | |

FAQs

What is the role of heat and work in the generic thermodynamic process shown with PV diagrams?

Heat is added or taken away, and work is done on or by the gas. The process changes internal energy, leading to new temperature, pressure, and volume states.

How do pistons and cylinders relate to gas compression and expansion?

The piston moves up and down in the cylinder while the gas is trapped underneath. Pushing down compresses the gas into a smaller volume; pulling up lets it expand into a larger volume, and the piston’s motion involves work.

How is the amount of work done computed for an isobaric (constant-pressure) process?

Use P = F/A and W = Fd, giving W = PAd. Since Ad equals the volume change ΔV, the result is W = PΔV. The work matches the area under the pressure–volume curve.

How does the sign of work depend on a cyclic P-V diagram?

In a cyclic process, the gas returns to its original state. If the cycle is clockwise, work is done by the gas, so the work is negative; the enclosed area on the closed curve gives the work per cycle.

Oct 25, 2026

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