Thermodynamic Processes

Overview

Thermodynamic Processes studies how gases change state through heating, cooling, compression, or expansion.

A state is described by pressure $p$, volume $V$, and temperature $T$. A process is a path from one state to another.

Definition

A thermodynamic process is any change in the state of a system involving pressure, volume, temperature, or internal energy.

The common JC processes are isochoric, isobaric, isothermal, adiabatic, and cyclic.

This wiki uses:

$$\Delta U=Q+W$$

where $Q$ is heat supplied to the system and $W$ is work done on the system. Work done by the gas is:

$$W_{\text{by}}=-W$$

Why It Matters

Recognising the process quickly identifies which quantity is constant, whether work is zero, whether heat transfer is zero, whether internal energy changes, and what graph shape to expect.

Key Representations

Isochoric means constant volume:

$$\Delta V=0$$

No boundary movement means:

$$W=0$$

so:

$$\Delta U=Q$$

The graph is a vertical line on a $p$-$V$ diagram.

Isobaric means constant pressure:

$$p=\text{constant}$$

Work done by the gas:

$$W_{\text{by}}=p\Delta V$$

so:

$$W=-p\Delta V$$

The graph is a horizontal line.

Isothermal means constant temperature:

$$T=\text{constant}$$

For an ideal gas:

$$pV=\text{constant}$$

and:

$$\Delta U=0$$

so:

$$Q=W_{\text{by}}$$

The graph is a rectangular hyperbola.

Adiabatic means no heat transfer:

$$Q=0$$

so:

$$\Delta U=W$$

Compression increases internal energy and temperature. Expansion decreases internal energy and temperature.

A cyclic process returns to the original state:

$$\Delta U=0$$

so:

$$Q_{\text{net}}+W_{\text{net}}=0$$

The graph is a closed loop.

Area under a process curve gives work done by gas:

$$W_{\text{by}}=\int pdV$$

See p-V Diagrams and Cycles.

Common Exam Traps

Isothermal does not mean no heat transfer. For an ideal gas, $\Delta U=0$, but heat may enter or leave.

Adiabatic means $Q=0$, not constant temperature.

Isochoric means constant volume, not constant pressure.

Same initial and final states means same $\Delta U$, but not necessarily same $Q$ or $W$.

A cyclic process can produce non-zero net work equal to the enclosed area.

Expansion gives $W<0$ under the convention $\Delta U=Q+W$ because the work done on the system is negative.

Links

• Thermal Physics B
• First Law and Thermodynamic Processes
• Ideal Gases
• p-V Diagrams and Cycles
• Molecular Motion