JEE/NEET Physics · Thermodynamics series · Part 3 of 6 · All parts →
- Adiabatic: NO heat exchange (fast or insulated) — Q = 0, so W = −ΔU
- Adiabatic relation: PV^γ = constant (γ = C_p/C_v)
- Adiabats are STEEPER than isotherms — the gas cools as it expands
- Expansion adiabatic: gas cools (work paid from savings); compression: heats
- γ: monatomic 5/3, diatomic 7/5 — the molecule’s shape sets its savings rate
Open a fizzy drink and the gas puff feels cool. Pump a bicycle tyre and it warms. Both are adiabatic — so fast (or so insulated) that heat has no time to move. The gas pays its own bills from internal savings. Part 3 of the Thermodynamics series.
- What ‘adiabatic’ really means
- PV^γ and the steep curve
- Heating by compression
- γ: the molecule’s fingerprint
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
What ‘Adiabatic’ Really Means
Adiabatic = Q = 0: no heat enters or leaves, either because the change is fast (engine strokes, milliseconds) or the container is insulated. The first law collapses to W = −ΔU: the gas’s work is funded entirely by its own internal energy — expansion cools it, compression heats it.
PV^γ and the Steep Curve
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| γ (gamma) | heat capacity ratio C_p/C_v | monatomic 5/3 ≈ 1.67, diatomic 7/5 = 1.4 |
| Q | heat exchanged in adiabatic process | exactly zero |
| ΔU | internal energy change | = −W (the entire budget) |
Heating by Compression
Squeeze a gas quickly and the piston’s work lands in U: temperature climbs by TV^(γ−1) bookkeeping. Diesel engines rely on this alone — compression heats fuel-air to ignition point, no spark plug needed.
γ: The Molecule’s Fingerprint
Monatomic gases (helium): only 3 translational jiggles, γ = 5/3. Diatomic (air, O₂): two rotational extras, γ = 7/5. More ways to store heat → smaller γ. This is the Kinetic Theory chapter peeking through (next series!).
Solved Examples
Gas expands rapidly out of the can — near-adiabatic, Q ≈ 0.
Work of expansion is paid from U: the gas (and can) cools.
✔
Answer: Adiabatic expansion → cooling
TV^(γ−1) = const: T₂/T₁ = (V₁/V₂)^(γ−1) = 8^0.4.
8^0.4 ≈ 2.3 — the gas more than doubles its kelvin temperature.
✔
Answer: T₂ ≈ 2.3 T₁
T₂ = 300 × 16^0.4 = 300 × 3.03 ≈ 910 K ≈ 637 °C.
Above diesel’s ignition point (~500 °C) — which is exactly why diesel engines need no spark plug.
✔
Answer: ≈910 K
- Using PV = const for adiabats. That’s the isotherm; adiabats carry PV^γ and cool on expansion.
- ‘Adiabatic = isothermal’ confusion. Opposite moods: isothermal exchanges heat freely, adiabatic exchanges none.
- Wrong γ. Air is diatomic (1.4), helium monatomic (1.67) — γ is the molecule’s business card.
- Forgetting which way T moves. Adiabatic expansion ALWAYS cools, compression ALWAYS heats — no exceptions.
This Physics in Your Daily Life
- Clouds form as air rises — rising air expands adiabatically in lower pressure, cools ~10 °C/km, water condenses: weather from PV^γ.
- Diesel engines need no spark plug — pure compression heating lights the fuel: adiabatic squeezing as an ignition system.
- Deodorants and fire extinguishers feel cold — rapid (adiabatic) expansion spending internal energy on work.
- Football pumping warms the pump — fast compression deposits your muscle work as internal energy.
- Scuba tanks cool as air is drawn down — and diver’s air warms on descent through regulators: the dive industry manages adiabatic swings.
Heat is a slow merchant — it seeps through walls at nature’s leisure. Squeeze or let fly fast enough and the transaction simply cannot complete before the deed is done: the gas’s state changes with its wallet untouched. ‘Adiabatic’ isn’t about insulation alone; it’s about outrunning the bookkeeper.
Air bursting from 5 atm to 1 (γ = 1.4): T drops by factor 5^0.28 ≈ 1.58 — room-temperature air exits near −80 °C. Same expansion done slowly with a heater would stay at 20 °C: the difference between the two moods, in degrees.
On P-V graph paper: draw an isotherm (hyperbola) and an adiabat through the same point — the adiabat plunges steeper (exponent γ > 1). Expanding along the steep curve drops you below the original isotherm: the picture of cooling. Compressing along it climbs above: heating drawn.
Practice set (answers hidden — try first)
(NEET-level) Adiabatic expansion: the gas
(JEE Main-level) γ for helium (monatomic):
(NEET-level) In adiabatic processes, Q =
(Concept) Which curve is steeper at a point: isotherm or adiabat?
(JEE Main-level) Air (γ=1.4) compressed 32× adiabatically: T ratio =
- adiabatic: Q = 0, W = −ΔU
- PV^γ = const, TV^(γ−1) = const
- adiabats steeper than isotherms
- expansion cools, compression heats
- γ: mono 5/3, dia 7/5
- 🔁 adiabatic meaning (speed/insulation)
- 🔁 PV^γ relations
- 🔁 compression heating examples
- 🧠 Chant: ‘fast = no heat = pay yourself’.
- 🧠 Steepness test: ‘steeper than isotherm = adiabat’.
- 🏠 Daily: clouds form by adiabatic cooling of rising air.
- 🏠 Daily: diesel ignites by compression alone.
Quick revision
- Adiabatic: NO heat exchange (fast or insulated) — Q = 0, so W = −ΔU
- Adiabatic relation: PV^γ = constant (γ = C_p/C_v)
- Adiabats are STEEPER than isotherms — the gas cools as it expands
- Expansion adiabatic: gas cools (work paid from savings); compression: heats
- γ: monatomic 5/3, diatomic 7/5 — the molecule’s shape sets its savings rate
- What ‘adiabatic’ really means
Have a doubt on this topic?
