What Is an Adiabatic Process in a Monatomic Ideal Gas?

An adiabatic process is a thermodynamic change in which no thermal energy is transferred between a gas and its surroundings, so $Q=0$. For a monatomic ideal gas, expansion lowers its temperature, while compression raises its temperature.

This is IB Physics HL-only content from B.4 Thermodynamics.

The Mechanism

The IB sign convention for the first law of thermodynamics is

$$Q=\Delta U+W,$$

where $W$ is work done by the gas. Because an adiabatic process has $Q=0$,

$$\Delta U=-W.$$

During adiabatic expansion, the gas does positive work on its surroundings, so $W>0$. Therefore, $\Delta U<0$. For a monatomic ideal gas,

$$\Delta U=\frac{3}{2}nR\Delta T,$$

so a decrease in internal energy means $\Delta T<0$: the gas cools.

During adiabatic compression, the surroundings do work on the gas. Work done by the gas is negative, so $W<0$, giving $\Delta U>0$ and therefore a temperature increase.

For a reversible adiabatic process in a monatomic ideal gas,

$$PV^{5/3}=\text{constant}.$$

The exponent $5/3$ is the adiabatic index $\gamma$ for a monatomic ideal gas. This relation means pressure falls more rapidly during expansion than it would at constant temperature. For example, if the volume doubles, $P_2=P_1(V_1/V_2)^{5/3}=P_1(1/2)^{5/3}\approx0.315P_1$. Therefore, an initial pressure of falls to about , assuming a reversible adiabatic change. The data booklet supplies the relevant thermodynamic equations, so focus on selecting and applying them correctly.

A common misconception is that adiabatic means constant temperature. It does not: adiabatic means $Q=0$, whereas isothermal means $\Delta T=0$. On a pressure-volume diagram, an adiabatic curve is steeper than an isothermal curve because the temperature also changes.

Exam Technique

For an Explain question, link the stages explicitly: $Q=0$, work changes internal energy, and internal energy determines temperature. Always use the IB convention $Q=\Delta U+W$, with $W$ defined as work done by the gas; reversing this sign convention is a common source of lost marks.