Thermodynamics

Six topics on what temperature actually measures and where the energy goes. Kinetic theory, which makes temperature the average kinetic energy of one particle and pressure a rate of momentum delivery, the ideal gas law and the constraint that earns you each shortcut, thermal transfer and what equilibrium does and does not switch off, the first law with its sign convention nailed down, specific heat and conduction rate as separate questions, and entropy, which supplies the direction that energy conservation never does.

AP exam 15-18%6 topics

Topics

9.1

Kinetic Theory of Temperature and Pressure

The Ideal Gas Law

Thermal Energy Transfer and Equilibrium

The First Law of Thermodynamics

Specific Heat and Thermal Conductivity

Entropy and the Second Law of Thermodynamics

Lesson

Diagnostic

after diagnostic

Key forms For every problem in this unit

Pressure

P = F⊥ / A, in pascals. Defined at every point INSIDE the gas, not only where it touches a wall

Average kinetic energy

K(avg) = (3/2) k_B T, per PARTICLE. k_B = 1.38 × 10⁻²³ J/K

Root-mean-square speed

v(rms) = √(3k_B T / m) = √(3RT / M). Speed goes as √T, so 4× the temperature doubles it

Same T, two gases

equal K(avg) per particle, NOT equal speed. Heavier particles move slower by √(m₂/m₁)

Ideal gas law

PV = nRT = N k_B T. R = 8.31 J/(mol·K). T is ALWAYS in kelvins

Two states, fixed n

P₁V₁ / T₁ = P₂V₂ / T₂. Cancel only what the setup pins: rigid tank cancels V, free piston cancels P

Kelvin conversion

T(K) = T(°C) + 273. A ratio in °C means nothing

Model assumptions

particle volume negligible, no appreciable force BETWEEN collisions, collisions elastic and frequent. Those wall collisions ARE the pressure

Speed distribution

Maxwell-Boltzmann: a spread, not one speed. Heating moves population right and flattens the curve; the area is the fixed particle count

First law

ΔU = Q + W, with W the work done ON the gas

Work on the gas

W = −PΔV at constant pressure. Compression gives W > 0. On a sloped path use the AREA under the curve

Internal energy

U = (3/2)nRT for a monatomic ideal gas. Depends on TEMPERATURE alone, so ΔU is path independent

Named processes

isothermal: ΔU = 0, Q = −W · adiabatic: Q = 0, ΔU = W · isovolumetric: W = 0, ΔU = Q · isobaric: W = −PΔV

Closed cycle

ΔU = 0, so Q(net) = −W(net). The enclosed area sets how big both are

Heating a substance

Q = mcΔT, so ΔT = Q / (mc). Larger c means a SMALLER temperature change

Mixing, insulated

m₁c₁(T(f) − T₁) + m₂c₂(T(f) − T₂) = 0. T(f) lands nearer the larger mc, not at the midpoint

Conduction rate

Q / Δt = kAΔT / L, in watts. A RATE, not an amount and not a temperature. Energy = rate × time

Entropy

ΔS = Q / T. The total for an ISOLATED system cannot decrease; a system trading energy with its surroundings certainly can

Direction

energy moves spontaneously from higher TEMPERATURE to lower, whatever the totals are. The first law permits both directions; the second picks one

Unit 9 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items drawn from across all 6 topics, with guaranteed misconception-code coverage. Identifies which misconceptions still bite when you cannot see which topic the question came from.