Thermodynamic Processes | Isothermal, Adiabatic & Cyclic Processes

Thermodynamic Processes | Advanced Thermal Physics

Advanced Physics → Advanced Thermal Physics → Thermodynamic Processes

Pressure–volume diagram showing different thermodynamic processes — Thermodynamic processes describe how macroscopic variables evolve during energy exchange.

Core idea
A thermodynamic process defines a specific path between equilibrium states, governed by heat transfer, work done, and internal energy change.

1. Isothermal Process

In an isothermal process, temperature remains constant. Heat exchange with the surroundings compensates exactly for work done by or on the system.

$PV = \text{constant}$

Isothermal pressure–volume curve — Isothermal expansion follows a hyperbolic path on a P–V diagram.

2. Isobaric Process

In an isobaric process, pressure remains constant. The system expands or contracts as temperature changes.

$W = P \Delta V$

Isobaric pressure–volume diagram — Isobaric processes appear as horizontal lines on a P–V graph.

3. Isochoric Process

In an isochoric process, volume remains constant. No work is done, and all heat supplied changes internal energy.

$W = 0$

Isochoric pressure–volume diagram — Isochoric processes are vertical lines on a P–V diagram.

4. Adiabatic Process

An adiabatic process occurs without heat exchange. Changes in internal energy arise solely from work done.

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

Comparison of adiabatic and isothermal curves — Adiabatic curves are steeper than isothermal curves.

5. Cyclic Process

A cyclic process returns the system to its initial state. Net work done equals the net heat exchanged over the cycle.

Cyclic process pressure–volume loop — The enclosed area in a P–V cycle represents net work done.

Cyclic processes form the basis of heat engines and refrigerators.

Level 1 — Conceptual

Problem 1. Define constraint motion. Give one everyday example.

Solution

Constraint motion refers to the motion of objects that are connected or restricted in such a way that the motion of one object affects the motion of another.

Example: Two blocks connected by a string over a pulley.

Problem 2. Why do two blocks connected by an inextensible string have the same magnitude of acceleration?

Solution

An inextensible string does not stretch, so any displacement of one block must produce an equal displacement of the other block in the opposite direction. Hence, their accelerations are equal in magnitude.

Level 2 – Numerical

Problem 3. Two blocks of masses 2 kg and 3 kg are connected by a light string over a smooth pulley. Find the acceleration of the system. (Take g = 10 m/s²)

Solution

Net driving force = (3 − 2)g = 1 × 10 = 10 N
Total mass = 2 + 3 = 5 kg

Acceleration,
a = F / m = 10 / 5 = 2 m/s²

Problem 4. A block rests on a smooth table and is connected to a hanging mass. Explain why both masses have the same acceleration.

Solution

The string is light and inextensible, so its length remains constant. Any motion of one mass immediately produces motion in the other, resulting in the same acceleration for both masses.

Level 3 — Advanced

Problem 5. In a system of three blocks connected in a straight line on a smooth surface, an external force F is applied to the last block. Find the acceleration of the system.

Solution

Let the masses be m₁, m₂, and m₃.
Total mass of the system = m₁ + m₂ + m₃

Using Newton’s second law for the whole system:
a = F / (m₁ + m₂ + m₃)

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