An adiabatic process has no heat transfer between system and surroundings. Work is performed at the expense of internal energy, so expansion cools a gas and compression warms it.
Learning Outcomes
No heat is transferred: Q = 0.
The first law reduces to W = −ΔU.
Adiabatic expansion lowers internal energy and temperature.
Adiabatic compression raises internal energy and temperature.
The process is rapid or the system is thermally insulated.
For an ideal gas, PVᵞ = constant; the P–V curve is an adiabat.
Intermediate Level
Condition and First-Law Reduction
In an adiabatic process no heat passes between the system and surroundings. Energy can still cross the boundary as work.
Key equation
Q=0
Key equation
0=Δ U+W
Key equation
W=-Δ U
Expansion and Compression
Change
W by gas
ΔU
Temperature
expansion
positive
negative
falls
compression
negative
positive
rises
Adiabatic Gas Relation
Key equation
PVγ=constant
Here γ is the ratio of heat capacities. An adiabat is steeper than an isotherm on the same P–V axes because temperature changes during adiabatic expansion or compression.
How It Is Achieved
Perform the change rapidly so heat has no time to flow.
Use thermal insulation to suppress heat transfer.
Examples include sound-wave compressions and expansions, rising atmospheric air, and interstellar gas-cloud changes.
Adiabatic Expansion
A gas expands adiabatically and does 180 J of work. Find Q and ΔU.
1
Working
Adiabatic condition: Q = 0
2
Step 2
ΔU = Q − W
3
Step 3
ΔU = 0 − 180 J
Final answer:Q = 0 and ΔU = −180 J
Common Mistakes
Adiabatic means Q = 0, not constant temperature.
A gas can do work even when no heat enters.
Expansion cools and compression warms an ideal gas adiabatically.
Use PVᵞ = constant, not Boyle’s PV = constant.
Short-Question Preparation
Q. Define an adiabatic process.
A. A process with no heat transfer between the system and surroundings.
Q. How does the first law reduce?
A.Q = 0 gives W = −ΔU.
Q. Why does adiabatic expansion cool a gas?
A. The gas supplies work from its internal energy.
Q. Write the ideal-gas adiabatic relation.
A.PVᵞ = constant.
Sticky Notes
No heat is transferred: Q = 0.
The first law reduces to W = −ΔU.
Adiabatic expansion lowers internal energy and temperature.
Adiabatic compression raises internal energy and temperature.
The process is rapid or the system is thermally insulated.
For an ideal gas, PVᵞ = constant; the P–V curve is an adiabat.
60-Second Revision
Adiabatic means Q = 0. Therefore W = −ΔU. Expansion does positive work, reduces U and cools the gas; compression raises U and temperature. The ideal-gas relation is PVᵞ = constant.
Summary
An adiabatic process has no heat transfer between system and surroundings. Work is performed at the expense of internal energy, so expansion cools a gas and compression warms it.
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.
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Exam preparation
Exam Focus
Important points
No heat is transferred: Q = 0.
The first law reduces to W = −ΔU.
Adiabatic expansion lowers internal energy and temperature.
Adiabatic compression raises internal energy and temperature.
The process is rapid or the system is thermally insulated.
For an ideal gas, PVᵞ = constant; the P–V curve is an adiabat.
Common mistakes
Adiabatic means Q = 0, not constant temperature.
A gas can do work even when no heat enters.
Expansion cools and compression warms an ideal gas adiabatically.
Use PVᵞ = constant, not Boyle’s PV = constant.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
Adiabatic Process
Sticky Notes · Quick Revision
1.
Key Point 1
No heat is transferred: Q = 0.
2.
Key Point 2
The first law reduces to W = −ΔU.
3.
Key Point 3
Adiabatic expansion lowers internal energy and temperature.
4.
Key Point 4
Adiabatic compression raises internal energy and temperature.
