Thermodynamics and the First Law

Thermodynamics in AP Physics 2 comes down to one equation used carefully and one kind of graph read carefully. Most lost points come from the sign of work.

The ideal gas law

PV = nRT = Nk_BT

Temperature must be in kelvin. The temperature of an ideal gas measures the average kinetic energy of its molecules, and its internal energy depends only on temperature.

The first law and its sign convention

ΔU = Q + W

In AP Physics 2, W is the work done on the gas.

• Q > 0 when heat flows into the gas.
• W > 0 when the gas is compressed; W < 0 when it expands.
• For a constant pressure process, W = −PΔV.

Other textbooks write ΔU = Q − W with W done by the gas. Both are correct; mixing them is not. Pick the AP form and keep it.

PV diagrams

The magnitude of the work equals the area under the curve on a PV diagram.

For a complete cycle the gas returns to its starting state, so ΔU = 0 and the net work equals the area enclosed by the loop.

Worked example

A gas at a constant pressure of 2.0 × 10⁵ Pa expands from 0.010 m³ to 0.025 m³ while absorbing 5000 J of heat.

1. Work done on the gas: W = −PΔV = −(2.0 × 10⁵)(0.015) = −3000 J. The gas expands, so the work on it is negative.
2. First law: ΔU = 5000 + (−3000) = 2000 J.
3. Internal energy rises, so the temperature of the gas rises.

Reasoning without numbers

• In an adiabatic expansion the gas does work with no heat coming in, so its internal energy and temperature fall.
• In an isothermal compression the internal energy stays the same, so all the work done on the gas leaves as heat.
• If P doubles and V halves, PV is unchanged, so the temperature is unchanged.

The free response approach

State the sign convention you use, identify the process type from the graph before calculating, and when asked about temperature, argue through PV = nRT or through ΔU.