Topic 8.4.18 min read
Isothermal Process
An isothermal process occurs at constant temperature. For an ideal gas, internal energy remains constant, so heat supplied equals work done by the gas.
Choose Your Level
Beginner Level
In an isothermal change the temperature stays fixed. If an ideal gas expands and does work, it must absorb the same amount of heat to prevent cooling.
Recommended for Class 11
Isothermal Process
Overview
An isothermal process occurs at constant temperature. For an ideal gas, internal energy remains constant, so heat supplied equals work done by the gas.
Learning Outcomes
- Temperature remains constant: ΔT = 0.
- For an ideal gas, ΔU = 0.
- The first law reduces to Q = W.
- A slow expansion permits heat transfer that maintains temperature.
- For fixed gas amount, PV = constant.
- The P–V curve is called an isotherm; area under it is work.
Intermediate Level
Condition and First-Law Reduction
For an ideal gas, internal energy depends only on temperature. Because temperature is unchanged in an isothermal process, ΔU = 0.
Pressure–Volume Relation
A fixed amount of ideal gas follows Boyle’s law during an isothermal change.
Graph and Rate
An isotherm slopes downward on a P–V graph, and the area under the curve represents work. The process should occur slowly enough for heat to pass between the system and surroundings and hold temperature constant.
| Isothermal expansion | Isothermal compression |
|---|---|
| V rises and P falls | V falls and P rises |
| gas does positive work | work by gas is negative |
| heat enters gas | heat leaves gas |
Energy Balance
An ideal gas expands isothermally and does 240 J of work. Find ΔU and Q.
Isothermal ideal gas: ΔU = 0
Q = ΔU + W
Q = 0 + 240 J
Final answer: ΔU = 0 and Q = +240 J
Examples
- Melting ice at 0 °C during the phase change
- Melting and evaporation carried out at constant temperature
- Slow gas expansion while in thermal contact with a reservoir
Common Mistakes
- Constant temperature does not mean Q = 0.
- For an ideal gas, ΔU = 0 because T is constant.
- An isothermal gas change should be slow enough for heat exchange.
- Do not draw an isotherm as a horizontal line.
Short-Question Preparation
Q. Define an isothermal process.
A. A thermodynamic process in which temperature remains constant.
Q. How does the first law reduce?
A. For an ideal gas ΔU = 0, so Q = W.
Q. Why is the process slow?
A. Heat needs time to flow and keep temperature constant.
Q. What is an isotherm?
A. The P–V curve representing an isothermal process.
Sticky Notes
- Temperature remains constant: ΔT = 0.
- For an ideal gas, ΔU = 0.
- The first law reduces to Q = W.
- A slow expansion permits heat transfer that maintains temperature.
- For fixed gas amount, PV = constant.
- The P–V curve is called an isotherm; area under it is work.
60-Second Revision
Isothermal means ΔT = 0. For an ideal gas, ΔU = 0, so Q = W. The gas follows PV = constant; its P–V curve is an isotherm and the area under it is work.
Summary
An isothermal process occurs at constant temperature. For an ideal gas, internal energy remains constant, so heat supplied equals work done by the gas.
Ask-the-Tutor Modes
- Explain the energy transfers simply.
- Apply the textbook sign convention.
- Derive the reduced equation.
- Solve a numerical step by step.
- Explain the P–V graph.
- Test me with an MCQ.
Exam Focus
Exam Focus
Important points
- Temperature remains constant: ΔT = 0.
- For an ideal gas, ΔU = 0.
- The first law reduces to Q = W.
- A slow expansion permits heat transfer that maintains temperature.
- For fixed gas amount, PV = constant.
- The P–V curve is called an isotherm; area under it is work.
Important formulas
- ΔT = 0
- ΔU = 0
- Q = W
- PV = constant
Common exam traps
- Constant temperature does not mean Q = 0.
- For an ideal gas, ΔU = 0 because T is constant.
- An isothermal gas change should be slow enough for heat exchange.
- Do not draw an isotherm as a horizontal line.
Long question structure
Definition → condition → first-law reduction → graph → physical explanation → example.
Common Mistakes
Common Mistakes
- Mistake
Constant temperature does not mean Q = 0.
- Mistake
For an ideal gas, ΔU = 0 because T is constant.
- Mistake
An isothermal gas change should be slow enough for heat exchange.
- Mistake
Do not draw an isotherm as a horizontal line.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Temperature remains constant: ΔT = 0.
For an ideal gas, ΔU = 0.
The first law reduces to Q = W.
A slow expansion permits heat transfer that maintains temperature.
An isothermal process occurs at constant temperature. For an ideal gas, internal energy remains constant, so heat supplied equals work done by the gas.
- Definition
- An isothermal process occurs at constant temperature. For an ideal gas, internal energy remains constant, so heat supplied equals work done by the gas.
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Exam Practice
Important Question
Q1. Define an isothermal process.
Important Question
Q2. How does the first law reduce?
Important Question
Q3. Why is the process slow?
Important Question
Q4. What is an isotherm?