Isothermal vs Adiabatic Process: Definition, Examples, and PV Graphs
Difference Between Isothermal And Adiabatic Process is a frequent topic in JEE Main Physics, key to accurate answers in thermodynamics. Both processes describe how a gas changes under specific conditions, but differ in how heat and temperature behave. For isothermal process, the temperature of the system remains constant while heat flows in or out. In contrast, adiabatic process does not allow heat exchange, so temperature changes as internal energy shifts. Mastery of differentiating these is vital for tackling numericals and interpreting PV diagrams correctly in exam questions.
In a real-world context, an ice cube melting at room temperature follows an isothermal process , as temperature stays at 0°C during phase change while heat is absorbed. Rapid compression of a bicycle pump demonstrates an adiabatic process, as the temperature of air increases due to lost work but no time for heat exchange. These differences reflect practical scenarios and are directly testable in JEE Main questions.
Difference Between Isothermal and Adiabatic Process: Key Attributes
| Attribute | Isothermal Process | Adiabatic Process |
|---|---|---|
| Definition | Temperature remains constant (ΔT = 0) | No heat is exchanged (Q = 0) |
| Heat Exchange | Occurs with surroundings | Completely insulated; no heat transfer |
| Equation | PV = constant | PVγ = constant |
| Internal Energy Change (ΔU) | ΔU = 0 (for ideal gas) | ΔU ≠ 0 (temperature changes) |
| Work Done (W) | W = Q = nRT ln(V2/V1) | W = [P2V2 – P1V1]/(1–γ) |
| Example | Melting ice, slow gas expansion in a thermostat bath | Quick piston compression, sound waves in air |
| PV Diagram Curve | Less steep than adiabatic | Steeper than isothermal |
Notice that the isothermal process allows heat exchange, keeping temperature steady, while the adiabatic process is perfectly insulated so all energy manifests as temperature change. Both are defined under the first law of thermodynamics, but apply different constraints on the gas.
PV Diagram Differences: Isothermal vs Adiabatic Process
On a pressure-volume (PV) diagram, the difference between isothermal and adiabatic process curves is a common JEE Main visual question. For an ideal gas, both curves show expansion/compression, but their shapes are distinct due to differences in heat and temperature behavior.
- Isothermal curve: PV = constant. Labeled as a shallower hyperbola.
- Adiabatic curve: PVγ = constant. Steeper than the isothermal for the same start/end volumes.
- The value of γ (gamma) is the ratio of specific heats (Cp/Cv) and affects the adiabatic slope.
- Both processes start at the same initial point, but adiabatic work done is less when expanding.
- Always label axes and note direction (expansion or compression) in JEE diagrams.
These curves help quickly identify which thermodynamic process is present in JEE Main numericals. Mastery allows fast elimination of wrong options.
Critical Formulae for Isothermal and Adiabatic Process
- Isothermal, ideal gas: PV = constant.
- Work done (W): W = nRT ln(V2/V1)
- Heat supplied Q = work done, ΔU = 0
- Adiabatic process: PVγ = constant.
- Work done: W = [P2V2 – P1V1]/(1 – γ)
- ΔU = –W (Q = 0), temperature changes
Remember, kinetic theory of gases always assumes perfect insulation for adiabatic, and a constant bath for isothermal. Formulae apply only to ideal gases.
How to Identify the Process: Exam Strategies
- If temperature is stated to remain constant, it’s isothermal.
- If system is insulated or process is very rapid, it’s adiabatic.
- If question says Q = 0 or no heat exchange, always choose adiabatic.
- Use process equations: does PV or PVγ stay constant?
- Look for words like “slowly in contact with thermal reservoir” (isothermal) or “sudden/rapid” (adiabatic).
Practice these distinctions in thermodynamics mock tests on Vedantu for strong exam revision.
Here’s a sample JEE-level example:
A gas expands from volume 2.0 L to 5.0 L at constant temperature T = 300 K. For 1 mole, calculate work done for the isothermal process. (R = 8.314 J/mol·K)
- W = nRT ln(V2/V1) = 1 × 8.314 × 300 × ln(5/2) ≈ 3641 J
Notice that the same process under adiabatic conditions would require knowledge of γ and no heat exchange would occur. This approach is standard in JEE Main practice papers.
Common Mistakes and Practical Applications of Isothermal and Adiabatic Process
- Confusing “no heat transfer” (adiabatic) with “constant temperature” (isothermal)—watch for these traps!
- Misreading the PV diagram (adiabatic steeper than isothermal at same points).
- Incorrectly applying formulas for heat/work in wrong context.
- Assuming real gases always follow these ideal equations – only true for ideal gas cases in JEE.
Practical uses include heat engines, refrigerators, and Bohr’s atomic model. Questions often ask to compare difference between isothermal and adiabatic process with examples, PV diagrams, or work calculations.
To deepen understanding, explore these related JEE Physics topics with Vedantu:
- first law of thermodynamics – energy conservation in all thermodynamic processes
- thermodynamics – laws and process types overview
- isobaric process – constant pressure alternative
The difference between isothermal and adiabatic process is a foundation of thermodynamics as tested in JEE Main Physics, and clear understanding ensures you solve related questions quickly and correctly. Keep practicing with Vedantu for accurate, exam-aligned preparation.
FAQs on Difference Between Isothermal and Adiabatic Process
1. What is the difference between isothermal and adiabatic process?
Isothermal process occurs at a constant temperature with heat exchange, while adiabatic process occurs without heat exchange, causing the temperature to change. Key points include:
- Isothermal: Temperature remains constant; heat is absorbed or released.
- Adiabatic: No heat exchange with surroundings; temperature changes.
- Examples: Melting ice (isothermal), rapid gas compression (adiabatic).
2. How to tell if a process is isothermal or adiabatic?
You can identify a process as isothermal or adiabatic by observing:
- Isothermal: Temperature stays constant throughout; heat exchange is allowed.
- Adiabatic: No heat is exchanged with surroundings; temperature changes.
- In problems, check wording like "insulated" (adiabatic) or "constant temperature" (isothermal), and examine if ΔT = 0 (isothermal) or Q = 0 (adiabatic).
3. Can a process be adiabatic but not isothermal?
Yes, a process can be adiabatic but not isothermal because in adiabatic processes, there is no heat exchange but the temperature changes. Features include:
- Adiabatic: Q = 0, but T changes as work is done on/by the system.
- Any rapid compression or expansion in an insulated system is adiabatic and not isothermal.
- Isothermal processes, in contrast, require temperature to be constant and heat to flow in or out.
4. What are real-world examples of isothermal and adiabatic processes?
Some practical examples of isothermal and adiabatic processes:
- Isothermal: Melting of ice at 0°C, slow expansion/compression of a gas in a thermostat bath, phase changes at constant temperature.
- Adiabatic: Sudden compression of air in a bicycle pump, rapid expansion of gases in an engine cylinder, air parcel rising in the atmosphere.
5. How do the PV diagrams differ for isothermal and adiabatic processes?
On PV diagrams, isothermal and adiabatic curves differ in steepness and shape:
- Isothermal: PV = constant, represented by a less steep hyperbola. Temperature does not change on the path.
- Adiabatic: PV𝛾 = constant, curve is steeper than isothermal for the same initial conditions because there's no heat exchange.
- Adiabatic curves fall more sharply due to temperature drop (during expansion) or rise (compression).
6. What is an isothermal process?
An isothermal process is a thermodynamic process in which the temperature of the system remains constant. Features include:
- ΔT = 0; the internal energy of an ideal gas does not change.
- Heat is exchanged with surroundings to maintain temperature as volume or pressure changes.
- Examples: Melting/boiling at constant temperature, slow gas expansion in a thermostat.
7. What is an adiabatic process?
An adiabatic process occurs when no heat is transferred between the system and its surroundings during the process. This means:
- Q = 0 (no heat exchange).
- Any change in internal energy is due to work done on or by the system.
- Examples: Sudden gas expansion/compression in insulated containers, fast piston movement.
8. What are the key formulae for isothermal and adiabatic processes?
Key formulas for these thermodynamic processes are:
- Isothermal Process (for Ideal Gas): PV = constant; Work done, W = nRT ln(Vf/Vi)
- Adiabatic Process: PV𝛾 = constant, where 𝛾 = Cp/Cv; Work done, W = (PfVf - PiVi)/(1-𝛾)
9. Why does temperature stay constant in an isothermal process even if volume changes?
In an isothermal process, temperature remains constant because any energy change due to work (expansion or compression) is exactly balanced by heat entering or leaving the system.
- If the gas expands, heat flows in to maintain temperature.
- If the gas is compressed, heat flows out to keep the temperature stable.
- This constant temperature is maintained by allowing heat exchange with the surroundings (a thermostat).
10. How do you identify isothermal and adiabatic processes in exam numericals?
To identify isothermal and adiabatic processes in exam problems:
- Look for terms "constant temperature" (isothermal) or "insulated", "no heat exchange" (adiabatic).
- Check if ΔT = 0 (isothermal) or Q = 0 (adiabatic) is stated or implied.
- If process occurs slowly and in contact with a heat reservoir, it's likely isothermal.
- If process is fast or insulated, it's likely adiabatic.
