Thermodynamics Formula Sheet & Cheat Sheet - IIT-JEE MAINS 2027

1. Fundamental Concepts & Ideal Gas State Equation

Thermodynamics focuses on macroscopic properties of systems in equilibrium. A clear understanding of system boundaries and equilibrium laws forms the baseline for IIT-JEE Mains numericals.

Classification of Systems

• Closed System: Mass remains constant within the boundary, while energy (heat and work) can cross the boundary.
• Open System: Both mass and energy cross the system boundary.
• Isolated System: Neither mass nor energy can cross the boundary of the system.

Zeroth Law of Thermodynamics

If body \(A\) is in thermal equilibrium with body \(C\), and body \(B\) is independently in thermal equilibrium with body \(C\), then body \(A\) and body \(B\) are in thermal equilibrium with each other. This law provides the operational definition of temperature.

Ideal Gas Equation of State

For an ideal gas containing \(n\) moles (or mass \(m\)), the state relation is given by:

Where \(P\) is absolute pressure, \(V\) is volume, \(T\) is absolute temperature, \(R\) is the universal gas constant, and \(R_{spec}\) is the specific gas constant.

2. First Law of Thermodynamics & Energy Conservation

The First Law is the principle of conservation of energy applied to thermodynamic systems.

Cyclic Process Form

For a closed system executing a complete thermodynamic cycle, the net heat transfer equals the net work done:

Non-Cyclic Process Form

For a finite change of state in a closed system, heat added \(Q\) minus total work done \(W\) yields the change in total stored energy:

Differential Form for Simple Compressible Systems

Ignoring macroscopic kinetic and potential energy variations, the differential internal energy \(dU\) is expressed as:

Enthalpy Definition

Enthalpy \(H\) is a thermodynamic state function defined as:

3. Second Law of Thermodynamics & Entropy Statements

The Second Law establishes the direction of spontaneous physical processes and introduces the state quantity entropy.

Classical Statements

• Kelvin-Planck Statement: It is impossible to construct a device operating in a cycle that produces no effect other than the extraction of heat from a single thermal reservoir and the performance of an equivalent amount of work.
• Clausius Statement: It is impossible to construct a device operating in a cycle that transfers heat from a colder body to a hotter body without external work input.

Entropy Change (\(\Delta S\))

For a reversible process between two equilibrium states, entropy change is defined by:

Inequality of Clausius

For any arbitrary closed cyclic process, the cyclic integral satisfies:

(Where equality holds strictly for reversible cycles, and strict inequality holds for irreversible cycles.)

4. Maxwell Thermodynamic Relations

Maxwell relations link primary thermodynamic properties \((P, V, T, S)\) using exact differentials derived from state functions \(U, H, F, G\):

5. Heat Capacities & Ratio of Specific Heats (\(\gamma\))

Molar Heat Capacities

Constant volume heat capacity \(C_v\):

Constant pressure heat capacity \(C_p\):

Adiabatic Index / Ratio of Specific Heats

The ratio of specific heat capacities \(\gamma\) is defined as:

6. IIT-JEE Mains PYQ Weightage & NTA Pattern Analysis

Thermodynamics forms a core section of both Physics and Chemistry in the IIT-JEE Mains paper pattern.

• Chapter Weightage: Expect 2 to 3 questions per shift directly testing First Law calculations, polytropic process work, indicator diagrams (\(P\)-\(V\) curves), or heat engine efficiency.
• NTA Pattern Trend: High emphasis on cyclic process area calculations, work done in isobaric/isochoric/adiabatic steps, and partial derivatives related to ideal gas expansions.
• PYQ Strategy: Practicing atmospheric pressure expansions, entropy sign determination, and mixture specific heat ratios ensures rapid accurate solutions.

7. Frequently Asked Questions (People Also Ask)