IMAT Physics · Heat and Thermodynamics

The First Law and Gas Processes

Heat given to a gas either raises its internal energy or comes out as work done by the gas; the four standard processes are special cases of that balance.

All Heat and Thermodynamics notes

Why this matters

A 2017 question gave the heat into a gas and the work it did and asked which kind of process it was. The gas questions from 2022 and 2023 also lean on knowing that an ideal gas held at constant temperature keeps its internal energy.

Concept 1 of 2: The first law of thermodynamics and the work done by a gas

Energy is never created or lost, only moved around. Heat put into a gas can go two ways: it can stay inside as extra internal energy, or the gas can spend it pushing a piston outwards. When a gas expands against a pressure it does work, and that work is the pressure times the change in volume.

Definition

First law: $\Delta U = Q - W$ , where $Q$ is the heat given to the gas and $W$ is the work done by the gas.
Signs: $Q > 0$ when heat goes in, $Q < 0$ when it comes out. $W > 0$ when the gas expands, $W < 0$ when it is compressed.
Some books write $\Delta U = Q + W$ , with $W$ the work done on the gas. The physics is the same; check which work is meant.
At constant pressure the work done by the gas is $W = p\Delta V$ . In general it is the area under the curve on a $p$ against $V$ graph.

First law and work at constant pressure

\Delta U = Q - W \qquad W = p\,\Delta V

$\Delta U$ change in internal energy of the gas, in J
$Q$ heat given to the gas, in J
$W$ work done by the gas, in J
$p,\ \Delta V$ pressure in Pa, change in volume in m³

Worked example

A gas at a constant pressure of

2.0 \times 10^5\ \text{Pa}

expands from 3.0 L to 5.0 L while absorbing 900 J of heat. Find the work it does and the change in its internal energy.

Practice this conceptself-check · 4 quick reps

Work done by the gas and work done on it have opposite signs

Compression means work is done on the gas, so the work done by the gas is negative. Putting 600 J of compression into

\Delta U = Q - W

+600

gives the internal energy change with the wrong sign.

Concept 2 of 2: Isothermal, isobaric, isochoric and adiabatic processes

Each named process holds one thing fixed, and that kills one term of the first law. Fix the temperature of an ideal gas and its internal energy cannot change. Fix the volume and no work is done. Block all heat flow and the only way to change the internal energy is through work.

Definition

Each process keeps one quantity constant:

Isothermal: constant temperature. For an ideal gas $\Delta U = 0$ , so $Q = W$ : all heat in comes out as work.
Isobaric: constant pressure, $W = p\Delta V$ .
Isochoric (isovolumetric): constant volume, $W = 0$ , so $Q = \Delta U$ .
Adiabatic: no heat exchanged, $Q = 0$ , so $\Delta U = -W$ . A gas that expands adiabatically cools; one compressed adiabatically warms. It happens when the change is fast or the container is insulated.

Process	What stays constant	First law becomes	Line on a p against V graph
Isothermal	Temperature, so the internal energy of an ideal gas	$Q = W$	A hyperbola, $pV$ constant
Isobaric	Pressure	$Q = \Delta U + p\Delta V$	A horizontal line
Isochoric	Volume, so no work is done	$Q = \Delta U$	A vertical line
Adiabatic	No heat in or out	$\Delta U = -W$	A curve steeper than the isotherm through the same point

Practice this conceptself-check · 4 quick reps

Adiabatic does not mean constant temperature

Adiabatic means no heat flows. The temperature changes, because work changes the internal energy. Isothermal is the opposite case: the temperature is constant, and heat does flow in or out.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

The first law of thermodynamics and the work done by a gas
First law and work at constant pressure
$\Delta U = Q - W \qquad W = p\,\Delta V$

Reference tables (1)

Isothermal, isobaric, isochoric and adiabatic processes4 rows

Process	What stays constant	First law becomes	Line on a p against V graph
Isothermal	Temperature, so the internal energy of an ideal gas	$Q = W$	A hyperbola, $pV$ constant
Isobaric	Pressure	$Q = \Delta U + p\Delta V$	A horizontal line
Isochoric	Volume, so no work is done	$Q = \Delta U$	A vertical line
Adiabatic	No heat in or out	$\Delta U = -W$	A curve steeper than the isotherm through the same point

Watch out for (2)

Work done by the gas and work done on it have opposite signs
→ The first law of thermodynamics and the work done by a gas
Adiabatic does not mean constant temperature
→ Isothermal, isobaric, isochoric and adiabatic processes

Drill the past-year questions on this topic

Open the bank with this topic pre-filtered.

Open in the bank