Topic 8.2.18 min read
Thermodynamic Work and P-V Diagrams
A gas transfers energy by doing pressure-volume work. At constant external pressure, work done by the gas is W = PΔV, and the area under a pressure-volume graph represents the work.
Choose Your Level
Beginner Level
When a gas expands, it pushes a piston and transfers energy to its surroundings. When it is compressed, the surroundings transfer energy to the gas.
Recommended for Class 11
Thermodynamic Work and P-V Diagrams
Overview
A gas transfers energy by doing pressure-volume work. At constant external pressure, work done by the gas is W = PΔV, and the area under a pressure-volume graph represents the work.
Learning Outcomes
- Pressure force on a piston is F = PA.
- Piston displacement changes volume by ΔV = AΔy.
- At constant pressure, W = PΔV.
- Expansion gives ΔV > 0 and positive work by the gas.
- Compression gives ΔV < 0 and negative work by the gas under the textbook convention.
- Area under a P-V curve equals work done by the gas.
Intermediate Level
Pressure-Volume Work
Consider gas in a cylinder with a movable frictionless piston of area A. External pressure P produces force F = PA. If the piston moves distance Δy, the volume changes by AΔy.
Here P is the external pressure and ΔV = V₂ − V₁. This simple form applies when external pressure is constant.
P-V Graph
On a graph of pressure against volume, a narrow strip has area P dV. Adding all strips gives the total work.
For constant pressure, the area is a rectangle: W = P(V₂ − V₁).
Textbook Sign Convention
| Process | ΔV | Work done by gas W | Energy description |
|---|---|---|---|
| Expansion | positive | positive | gas does work on surroundings |
| Compression | negative | negative | surroundings do work on gas |
| Constant volume | zero | zero | no boundary work |
Solved Examples
Constant-Pressure Expansion
A gas expands from 0.020 m³ to 0.050 m³ against 2.0 × 10⁵ Pa. Find work by the gas.
ΔV = 0.050 − 0.020 = 0.030 m³
W = PΔV
W = (2.0 × 10⁵)(0.030)
Final answer: W = +6.0 × 10³ J
Compression
A gas is compressed by 4.0 × 10⁻³ m³ at constant pressure 1.5 × 10⁵ Pa. Find W by the gas and work on the gas.
ΔV = −4.0 × 10⁻³ m³
Wby = PΔV
Wby = (1.5 × 10⁵)(−4.0 × 10⁻³)
Final answer: Work by gas = −600 J; work on gas = +600 J
Common Mistakes
- Use absolute temperature in kelvin.
- Convert all quantities to SI units.
- State the assumptions or sign convention before applying a formula.
Short-Question Preparation
Q. Derive W = PΔV.
A. Use F = PA, W = FΔy and ΔV = AΔy.
Q. How is work found from a P-V graph?
A. It is the area under the curve between the initial and final volumes.
Q. State the textbook sign convention.
A. Expansion gives positive work by the gas; compression gives negative work by the gas.
Q. When is W = PΔV directly applicable?
A. When the external pressure is constant.
Sticky Notes
- Pressure force on a piston is F = PA.
- Piston displacement changes volume by ΔV = AΔy.
- At constant pressure, W = PΔV.
- Expansion gives ΔV > 0 and positive work by the gas.
- Compression gives ΔV < 0 and negative work by the gas under the textbook convention.
- Area under a P-V curve equals work done by the gas.
60-Second Revision
A gas transfers energy by doing pressure-volume work. At constant external pressure, work done by the gas is W = PΔV, and the area under a pressure-volume graph represents the work.
Summary
A gas transfers energy by doing pressure-volume work. At constant external pressure, work done by the gas is W = PΔV, and the area under a pressure-volume graph represents the work.
Ask-the-Tutor Modes
- Explain it simply.
- Derive the equation.
- Solve a numerical.
- Check the sign convention.
- Test me with an MCQ.
Exam Focus
Exam Focus
Important points
- Pressure force on a piston is F = PA.
- Piston displacement changes volume by ΔV = AΔy.
- At constant pressure, W = PΔV.
- Expansion gives ΔV > 0 and positive work by the gas.
- Compression gives ΔV < 0 and negative work by the gas under the textbook convention.
- Area under a P-V curve equals work done by the gas.
Common exam traps
- Wrong sign or temperature scale
Long question structure
Definition → assumptions → derivation → result → interpretation.
Common Mistakes
Common Mistakes
- Mistake
Use the stated model and convention.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Pressure force on a piston is F = PA.
Piston displacement changes volume by ΔV = AΔy.
At constant pressure, W = PΔV.
Expansion gives ΔV > 0 and positive work by the gas.
A gas transfers energy by doing pressure-volume work. At constant external pressure, work done by the gas is W = PΔV, and the area under a pressure-volume graph represents the work.
- Definition
- A gas transfers energy by doing pressure-volume work. At constant external pressure, work done by the gas is W = PΔV, and the area under a pressure-volume graph represents the work.
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Exam Practice
Important Question
Q1. Derive W = PΔV.
Important Question
Q2. How is work found from a P-V graph?
Important Question
Q3. State the textbook sign convention.
Important Question
Q4. When is W = PΔV directly applicable?