Vedatom Physics
Thermo / Kinetic Theory
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Heat & work — sign convention
First law: ΔQ = ΔU + ΔW — heat supplied = rise in internal energy + work done by the gas.
Heat Q: + when supplied TO the system, − when released.
Work W: + when done BY the gas, − on compression.
For an ideal gas U is purely molecular kinetic energy — it depends on T alone.
Full walkthrough →
Thermo Lab · all topics
§01

The ideal-gas equation — squeeze it, heat it

One mole of gas lives in the chamber below. Push the piston in and the same molecules hit the walls more often — pressure climbs. Heat the gas and they hit harder and more often — pressure climbs again. The whole behaviour compresses into one line: PV = nRT.

piston
P = {{ gasP }} atm
V = {{ gasV }} L
T = {{ gasT }} K
volume V (piston){{ gasV }} L
temperature T{{ gasT }} K
P = nRTV = {{ gasP }} atm
n = 1 mol · R = 0.0821 L·atm·mol⁻¹K⁻¹. Same equation, other clothes: PV = NkT (per molecule) and P = ρRT/M (per density).
Boyle · T constant
PV = constant
halve the volume, double the pressure
Charles · P constant
V / T = constant
gases swell in proportion to absolute T
Gay-Lussac · V constant
P / T = constant
a sealed can in a fire builds pressure
§02

Where pressure comes from — the KTG derivation

Follow one molecule ricocheting between two walls a distance L apart. Each wall collision reverses its x-momentum; count the hits, average over the swarm, and pressure falls out. This four-line argument is the heart of kinetic theory — reproduce it on demand.

momentum handed to the wall per hit: Δp = 2mv_x · time between hits on the same wall: Δt = 2L / v_x
STEP 1 · one molecule
f = ΔpΔt = m v_x²L
average force one molecule puts on one wall
STEP 2 · all N, isotropy
F = Nm⟨v_x²⟩L · ⟨v_x²⟩ = ⟨v²⟩3
no direction is special — x gets a third of ⟨v²⟩
STEP 3 · divide by area
P = Nm⟨v²⟩3V = 13 ρ⟨v²⟩
macroscopic pressure from microscopic speed
STEP 4 · compare with PV = NkT
12 m⟨v²⟩ = 32 kT
temperature is kinetic energy — same for every gas at the same T
The assumptions doing the work: molecules are point masses, collisions are elastic, there are no intermolecular forces between collisions, and the time spent in a collision is negligible. Break these (high pressure, low temperature) and you get a real gas — see Going deeper.