In physics, the thermodynamic process describes how heat and energy move within a system.
One special type of process is the adiabatic process, where no heat is transferred between the system and its surroundings. This means the system changes in pressure, volume or temperature, but without gaining or losing heat. Adiabatic processes are important in topics like gas laws, engine cycles, and atmospheric studies, making them a key concept for students preparing for exams.

What is an Adiabatic Process?

An adiabatic process is when no heat is exchanged between a system and its surroundings.

Chemistry Notes Free PDFs

The word “adiabatic” comes from Greek, meaning “without heat transfer”. In this process, energy changes only as work, not heat. Key characteristics include rapid changes in pressure and temperature, as there’s no time for heat exchange. This can happen in situations like gas compression or when air cools as it rises in the atmosphere.

In an adiabatic process, the system does not exchange heat with its surroundings (Q=0). This means that any change in the system’s energy comes from work done, rather than heat transfer.

The relationship between internal energy is crucial: when work is done or by the system, it directly affects the internal energy, causing changes in temperature or pressure. An isentropic process is a special case of adiabatic process where the process is also reversible, meaning there’s no loss of energy due to friction or other factors, and entropy remains constant. This typically happens in ideal conditions, like in a perfect gas undergoing adiabatic compression or expansion.

Adiabatic Process Formula

In adiabatic conditions, all energy change happens through work, as there’s no heat transfer involved (Q=0). The pressure and volume of the system follow the relation PVr= constant, where 

Derivation of Adiabatic Equation

To understand how pressure and volume are related in an adiabatic process, we derive the equation PV^γ = constant. The equation shows that when no heat is exchanged the product of pressure (P) and volume (V) raised to the power of gamma(r) remains constant. Here r,(gamma) is the ratio of specific heats, defined as Cp/Cv, where Cp is the specific heat at constant pressure and Cv is the specific heat at constant volume. This relationship is useful in solving numerical problems and understanding gas behaviour under adiabatic conditions. You can also visualise with the PV graph, where the adiabatic curve is steeper than the isothermal one.

Adiabatic Relation Between P, V, And T

We will be deriving the relation between P, V, and T using the first law of thermodynamics which states that heat supplied to the system is capable of doing some work when the heat absorbed by the system is equal to the sum of the increase in internal energy and external work done on the surrounding by the system.

An essential condition for the adiabatic process

• The system and surroundings must not be exchanging heat for which the walls should be insulated.
• The process of expansion and compression so that the system should not be able to exchange heat with the surroundings.

Case I: Relation between P and V

According to the First Law of thermodynamics

K: constant

This equation gives the relation between P( Pressure) and V( Volume ) of Ideal Gas.

Case II: Relation between P and T

We know that

PV = RT [ for one mole of gas ]

Substituting the value of V in the equation

This equation gives the relation between P and T.

Case III: Relation between V and T

We know that

PV = RT [ for one mole of gas ]

Substituting the value of P in the equation

This equation gives the relation between V (Volume) and T (Temperature).

Derivation of Work Done In Adiabatic Process

Go through the below derivation of work done in the Adiabatic process and

Let there be a cylinder that has insulated walls and has a frictionless and insulated piston. It contains gas inside it. Also, the gas expands adiabatically.

n: number of moles of an ideal gas

P: the pressure of a gas

dx: small distance moved by a piston

dW: work is done by gas

A: cross-sectional area of a piston

dV= Adx: increase in the volume of gas

P1, V1, T1: Initial state of Gas

P2, V2, T2: Final state of Gas

Total Work done of the gas is given by:

Also, we know that P1V1 and P2V2 are equal to nRT1 and nRT2 respectively. So the equation for work done in the adiabatic process is also given by

Ace your exams and level up your preparation game with Testbook's curated study materials and exam practice sets. Download the Testbook App for free today to take advantage of some exclusive offers now.