LucidSTEM
A-LEVEL 9702 · A2 · TOPIC 16
Thermodynamics The chain of the topic: internal energy is the total of the random kinetic and potential energies of the molecules, a rise in temperature raises it, a gas pushing a piston does work W = pΔV, and the first law ΔU = q + W ties heat and work to that energy. Around the hexagon are the four ideas; above is what it builds on, below is where it leads.
TOPIC 16: THERMODYNAMICS
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
TheLucidSTEM · thelucidstem.com
BUILDS ON
T5 Energy: work and heat T14 Temperature scale T15 Ideal gases: pV and mean KE 16.1
16.1
16.2
16.2
TOPIC 16
THERMO-
DYNAMICS
1 · INTERNAL ENERGY
A microscopic energy store, not heat.
U = total random kinetic + potential energy of
all the molecules of the system.
A function of state: ΔU depends only on the
end states, never on the route taken.
For an ideal gas there is no molecular PE, so U is
entirely kinetic and fixed by temperature alone.
U = Σ (KE + PE) of molecules
random molecular
motion and
interactions
2 · TEMPERATURE & INTERNAL ENERGY
Warmer means more internal energy.
Raising the temperature raises the mean random
kinetic energy, and so the internal energy.
For an ideal gas: mean KE per molecule = (3/2)kT,
so U rises in direct proportion to T in kelvin.
Same temperature gives the same U, whatever
the pressure or volume of the gas.
U ∝ T (ideal gas, T in K)
U
T / K
0
U rises with T
3 · WORK DONE BY A GAS
An expanding gas pushes its boundary.
At constant pressure the gas does work W = pΔV
as it pushes a piston through a volume change.
Expansion (ΔV > 0): the gas does work on the
surroundings; compression (ΔV < 0): work in.
On a p–V diagram, work is the area under the line.
W = p ΔV
F = pA
gas, p
piston moves out
4 · THE FIRST LAW
Energy conservation for a gas.
ΔU = q + W: q is heat supplied to the gas,
W is work done on the gas. Watch the signs.
Constant volume: W = 0, so ΔU = q.
Isothermal (ideal gas): ΔU = 0, so q = −W.
Adiabatic (no heat flow): q = 0, so ΔU = W.
ΔU = q + W
gas
ΔU
q in
work out
heat in raises U or leaves as work
LEADS TO
T17 Oscillations: energy conserved as KE and PE swap T15 Ideal gases: (3/2)kT closes the U-to-T link T14 Temperature: heat capacity and change The thread is energy conservation: heat and work are two routes to the same change in a system's internal energy.
← Builds on IGCSE: Particle model of matter