Four thermodynamic processes describe how gases change state

Engineering Physics | AQA A-Level Physics

The four processes

There are four main thermodynamic processes, each defined by the quantity that stays constant:
- Isobaric (constant pressure): $\Delta p = 0$
- Isovolumetric / isochoric (constant volume): $W = 0$
- Isothermal (constant temperature): $\Delta T = 0$
- Adiabatic (no heat transfer): $Q = 0$

Key Definitions

Isobaric process: A process in which no change in pressure occurs.

Isovolumetric process: A process where no change in volume occurs and the system does no work.

Isothermal process: A process in which no change in temperature occurs.

Adiabatic process: A process where no heat is transferred into or out of the system.

Isobaric (constant pressure)

This occurs when gases expand or contract freely during a change in temperature.
On a p-V diagram, this is a horizontal line.
Since $\Delta p = 0$, the work done is $W = p\Delta V$.
From the first law: $Q = \Delta U \pm p\Delta V$
The $\pm$ reflects whether work is done on or by the gas due to the volume change.

Isovolumetric (constant volume)

If there is no change in volume, there is no work done on or by the gas, so $W = 0$.
On a p-V diagram, this is a vertical line.
From the first law: $Q = \Delta U + 0$, so $Q = \Delta U$.
All the heat energy supplied goes directly into changing the internal energy of the gas.

Isothermal (constant temperature)

If the temperature does not change, the internal energy of the gas does not change, so $\Delta U = 0$.
On a p-V diagram, this follows a curved line (a hyperbola, since $pV = \text{constant}$ for an ideal gas at constant temperature).
From the first law: $Q = 0 + W$, so $Q = W$.
The key part is that all heat supplied is converted into work, and all work done on the gas is released as heat.

Adiabatic (no heat transfer)

If no heat enters or leaves the system, then $Q = 0$.
From the first law: $0 = \Delta U + W$, so $W = -\Delta U$.
This means all the work done is at the expense of the system's internal energy.
An adiabatic process will therefore usually be accompanied by a change in temperature: adiabatic expansion causes cooling, adiabatic compression causes heating.
On a p-V diagram, the adiabatic curve is steeper than the isothermal curve.

Adiabatic equation for ideal gases

Adiabatic processes in ideal gases can be modelled by:

$$pV^{\gamma} = \text{constant}$$

Where $\gamma$ is the adiabatic index (ratio of specific heat capacities). For a monatomic ideal gas, $\gamma = \frac{5}{3}$.
This gives us: $p_1 V_1^{\gamma} = p_2 V_2^{\gamma}$
This equation allows you to calculate changes in pressure, volume and temperature during adiabatic processes.

Common Mistake

Students often confuse isothermal and adiabatic curves on p-V diagrams. Both curve downwards during expansion, but the adiabatic curve is always steeper. Think of it this way: in an adiabatic expansion, the gas cools as it expands (no heat input), so the pressure drops more rapidly than in an isothermal expansion where heat flows in to maintain the temperature.