Thermal Equilibrium Zeroth Law

8 MCQs9-step worked example

Source: NCERT ThermodynamicsPYQ coverage: NEET 2022, 2023, 2024, 2025Official key: NTA-verifiedLast reviewed: May 2026

Lesson

The trap you're walking into: NEET doesn't just ask "state the zeroth law." It tests whether you understand why thermal equilibrium is transitive and what the zeroth law actually establishes — the logical foundation for temperature as a measurable quantity. Aspirants who memorise the statement but miss its consequence (that temperature is a valid state variable) lose marks on conceptual questions.

What thermal equilibrium means. Two systems are in thermal equilibrium when, connected by a diathermic (heat-conducting) wall, no net heat flows between them. Their temperatures are equal. An adiabatic wall, by contrast, prevents heat exchange entirely — systems separated by an adiabatic wall are thermally isolated regardless of their temperatures (NCERT Class 11 Physics Chapter 11, page 2).

The zeroth law — and why it matters. If system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then A and B are in thermal equilibrium with each other. This transitivity property is not obvious — it is a physical law, not a mathematical tautology. Without it, you could not assign a single number (temperature) to characterise a system's thermal state and then use a thermometer (system C) to compare two other systems.

Why "zeroth"? The first and second laws of thermodynamics were formulated earlier. When physicists realised that the transitivity of thermal equilibrium was a logically prior assumption — required before the other laws made sense — they numbered it zero.

What NEET targets here:

Distinguishing diathermic vs adiabatic walls and their role in defining equilibrium.
Recognising that the zeroth law is the basis for the concept of temperature, not just a statement about heat flow.
Understanding that thermal equilibrium is about net heat flow being zero, not about systems being identical.

Practice MCQs

Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.

MCQ 1Easy RecallPractice

The zeroth law of thermodynamics is the basis for the concept of:

MCQ 2Easy RecallPractice

Two systems A and B are separated by an adiabatic wall. System A is at 400 K and system B is at 300 K. Which statement is correct?

MCQ 3Easy RecallPractice

A diathermic wall is one that:

MCQ 4Direct ApplicationPractice

System A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C. According to the zeroth law, which conclusion follows?

MCQ 5Direct ApplicationPractice

A thermometer works on the principle of:

MCQ 6Direct ApplicationPractice

Two bodies at different temperatures are brought into contact through a diathermic wall. At thermal equilibrium:

MCQ 7Easy RecallPractice

Which of the following pairs correctly matches wall type to its thermal property? (i) Diathermic wall — permits heat transfer (ii) Adiabatic wall — prevents heat transfer

MCQ 8Concept TrapPractice

The zeroth law of thermodynamics was numbered 'zero' because:

Worked Example

1
Given
Three metal blocks P, Q, and R are insulated from the environment. Block P (at an unknown temperature Tₚ) is placed in contact with block R through a diathermic wall and they reach thermal equilibrium at 350 K. Block Q (at an unknown temperature T_Q) is then placed in contact with block R through a diathermic wall and they also reach thermal equilibrium at 350 K.
2
Required
Determine whether blocks P and Q are in thermal equilibrium with each other, and state the law that justifies your answer.
3
Concept
The zeroth law of thermodynamics: if system P is in thermal equilibrium with system R, and system Q is in thermal equilibrium with system R, then P and Q are in thermal equilibrium with each other.
4
Formula
No algebraic formula is needed. The zeroth law is the governing principle: thermal equilibrium is transitive.
5
Substitution
- P is in thermal equilibrium with R (both at 350 K after contact). - Q is in thermal equilibrium with R (both at 350 K after contact). - By the zeroth law: P is in thermal equilibrium with Q.
6
Calculation
No numerical calculation required. The zeroth law directly yields the conclusion.
7
Final answer
Yes, P and Q are in thermal equilibrium with each other. Both are at 350 K. The zeroth law of thermodynamics justifies this conclusion.
8
Common trap
Aspirants sometimes confuse "same temperature" with "same internal energy." Two blocks at 350 K are in thermal equilibrium — but they may have very different internal energies if they differ in mass or specific heat capacity. The zeroth law guarantees equal temperature, not equal energy content.
9
Similar NEET-style question
Three gas containers X, Y, and Z are connected pairwise through diathermic walls. X and Z reach equilibrium; Y and Z reach equilibrium. Without the zeroth law, could you conclude X and Y are at the same temperature? (Answer: No — the zeroth law is precisely the physical assertion that this transitivity holds.) ---

Before solving, remember these

Law

Zeroth law of thermodynamics

If two systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other. Defines temperature operationally.

-- NCERT, p. 2

Formulas

4 formulas — click to collapse

Adiabatic relations for ideal gas

P V^{γ} = const; T V^{γ - 1} = const

Relations holding during reversible adiabatic process. gamma = Cp/Cv.

Symbol	Quantity	SI Unit
P	pressure	Pa
V	volume	m^3
T	temperature	K
gamma	adiabatic index	-

Valid when

Q = 0 (no heat exchange)
Quasi-static (reversible)
Ideal gas

First law of thermodynamics

Δ U = Q - W

Change in internal energy = heat ADDED minus work DONE BY the system. Energy conservation including thermal energy.

Symbol	Quantity	SI Unit
Delta_U	change in internal energy	J
Q	heat added to system	J
W	work done BY system	J

Valid when

Closed system (no mass exchange)
Sign convention: Q>0 heat in, W>0 system does work

Work done in isothermal process (ideal gas)

W = n R T ln \frac{V _{f}}{V _{i}}

Work done by ideal gas during isothermal expansion. Q = W (since Delta_U = 0). Reverse for compression.

Symbol	Quantity	SI Unit
n	moles	mol
R	gas constant 8.314	J/mol/K
T	temperature	K
V_i, V_f	initial/final volume	m^3

Valid when

Ideal gas
Quasi-static (reversible) isothermal

Mayer's relation (Cp - Cv = R)

C_{p} - C_{v} = R

For ideal gas: difference of molar specific heats equals gas constant R. Useful for converting between Cp and Cv.

Symbol	Quantity	SI Unit
Cp	molar specific heat at const P	J/mol/K
Cv	molar specific heat at const V	J/mol/K
R	8.314	J/mol/K

Valid when

Ideal gas
Per mole basis

Exam Traps & Common Mistakes

These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.

2 items — click to collapse

Trap

Adiabatic vs isothermal P-V curve

Category: Graph Interpretation

Student misidentifies which P-V curve is adiabatic (steeper) vs isothermal.

When it triggers

P-V graph showing one or more processes; question asks for process type.

How to avoid

Adiabatic curve is STEEPER than isothermal at the same point (slope ratio = γ). Adiabat: PV^γ; isotherm: PV = const.

Mistake

Identifies adiabatic curve as gentler than isothermal on P-V diagram (or vice versa).

Root cause: graph misread

Correction

Adiabatic curve is STEEPER than isothermal at the same P-V point. Slope ratio at same point: adiabatic / isothermal = γ. Memorise: 'adiabatic angles down sharper'.