Intermediate

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Thermodynamic Systems, Zeroth Law & Heat

Master Thermodynamics basics for JEE & NEET. Covers open/closed/isolated systems, Zeroth Law, heat vs work, state vs path functions, Cp Cv Mayer's relation, equipartition.

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Thermodynamics is the science of energy, heat, and work — and of the rules that govern their interconversion. It forms the theoretical foundation for understanding engines, refrigerators, chemical reactions, and the direction of natural processes. The chapter begins with careful definitions: what constitutes a system and its surroundings, how to measure temperature (the Zeroth Law), and the role of heat as a mode of energy transfer. These conceptual foundations, while often undervalued in rushed revision, are tested directly in JEE and NEET through questions about state variables, quasi-static processes, and the distinction between heat and internal energy. Getting this groundwork right makes the First Law, thermodynamic processes, and Carnot cycle all significantly easier to understand and apply.

1. Basic Terminology

Term	Definition
System	The specific part of the universe under study (e.g., gas in a cylinder).
Surroundings	Everything outside the system.
Open system	Exchanges both energy AND matter with surroundings (e.g., open beaker).
Closed system	Exchanges energy but NOT matter (e.g., gas in sealed piston).
Isolated system	Exchanges NEITHER energy nor matter (e.g., thermos flask — ideal).
State variables	Macroscopic properties that define the state: $P$ , $V$ , $T$ , $n$ , internal energy $U$ .
Equation of state	Relation connecting state variables; for ideal gas: $P V = n R T$ .
Equilibrium state	All state variables have definite, uniform values throughout the system.
Quasi-static process	Infinitely slow process — system passes through a continuous sequence of equilibrium states; reversible.

2. Zeroth Law of Thermodynamics

Statement: If two systems A and B are each in thermal equilibrium with a third system C, then A and B are in thermal equilibrium with each other.

If $A \leftrightarrow C$ and $B \leftrightarrow C$ then $A \leftrightarrow B$

Significance: The Zeroth Law provides the conceptual basis for the measurement of temperature. It establishes that temperature is a fundamental, well-defined property — two bodies in thermal equilibrium have the same temperature. This law was formulated after the First and Second Laws, hence it was named "Zeroth."

Thermal equilibrium: Two bodies are in thermal equilibrium when there is no net heat flow between them — meaning they are at the same temperature.

3. Heat, Work, and Internal Energy — Key Distinctions

Internal Energy ( $U$ )

The total energy stored within a system — sum of kinetic and potential energies of all constituent molecules.

For an ideal gas: internal energy depends only on temperature — $Δ U = n C_{v} Δ T$ . There is no intermolecular potential energy (molecules don't interact).
$U$ is a state function — its value depends only on the current state, not on how the state was reached.
$Δ U = 0$ for a cyclic process (returns to initial state).
$Δ U = 0$ for an isothermal process of an ideal gas ( $T$ constant $⟹ U$ constant).

Heat ( $Q$ ) and Work ( $W$ ) — Path Functions

Both $Q$ and $W$ are path functions — their values depend on the specific process taken, not just the initial and final states. Unlike $U$ , neither $Q$ nor $W$ is a property of the state itself.

Feature	Internal Energy ( $U$ )	Heat ( $Q$ )	Work ( $W$ )
Type	State function	Path function	Path function
Sign convention	—	$Q > 0$ : heat absorbed by system $Q < 0$ : heat released	$W > 0$ : work done BY system $W < 0$ : work done ON system
Formula	$Δ U = n C_{v} Δ T$ (ideal gas)	$Q = m c Δ T$ (calorimetry)	$W = \int P d V$ (expansion)

Work Done in Thermodynamic Processes

For a gas expanding against external pressure:

$W = \int_{V_{1}}^{V_{2}} P d V$

Graphically: Work = area under the $P - V$ curve. Expansion (volume increases) $⟹$ positive work done by gas. Compression $⟹$ negative work (work done on gas).

4. Molar Heat Capacities

Molar heat capacity at constant volume ( $C_{v}$ ): Heat needed to raise the temperature of 1 mole by 1 K at constant volume (no work done, all heat goes into internal energy).

Molar heat capacity at constant pressure ( $C_{p}$ ): Heat needed at constant pressure — part goes into internal energy, part into work of expansion.

$C_{p} - C_{v} = R (Mayer's relation, ideal gas)$

Gas type	$C_{v}$	$C_{p}$	$γ = C_{p} / C_{v}$	Examples
Monatomic	$\frac{3}{2} R$	$\frac{5}{2} R$	$\frac{5}{3} \approx 1.67$	He, Ar, Ne
Diatomic	$\frac{5}{2} R$	$\frac{7}{2} R$	$\frac{7}{5} = 1.40$	$O_{2}$ , $N_{2}$ , $H_{2}$ , air
Triatomic (linear)	$\frac{7}{2} R$	$\frac{9}{2} R$	$\frac{9}{7} \approx 1.29$	${CO}_{2}$ (at high temp)

Equipartition of energy: Each degree of freedom contributes $\frac{1}{2} k_{B} T$ per molecule (or $\frac{1}{2} R T$ per mole) to the internal energy. Monatomic: 3 translational DOF $⟹ U = \frac{3}{2} n R T$ . Diatomic (at moderate $T$ ): 5 DOF (3 translational + 2 rotational) $⟹ U = \frac{5}{2} n R T$ .

State Function vs Path Function — Never Confuse Again

Property	State function	Path function
Depends on	Initial and final state only	The specific process/path taken
Value for cyclic process	Zero (returns to same state)	Not necessarily zero
Examples	$P$ , $V$ , $T$ , $U$ , $S$ (entropy)	$Q$ (heat), $W$ (work)

JEE / NEET Power Tips — Systems, Zeroth Law & Heat

$Δ U = 0$ for an ideal gas in an isothermal process. The internal energy of an ideal gas depends only on temperature. If $T$ is constant, $Δ U = 0$ regardless of pressure or volume changes. This is the most important consequence of ideal gas behaviour in thermodynamics.
$Q$ and $W$ are path functions; $Δ U$ is a state function. You cannot physically say "the heat of a system" or "the work of a system" — only the change in internal energy is a property of the state. This distinction is the conceptual heart of the First Law.
Work = area under $P - V$ curve. For any process on a $P - V$ diagram, the work done equals the area between the curve and the volume axis. Expansion $⟹$ positive area $⟹$ positive work BY system. Compression $⟹$ negative work. This geometric interpretation is tested frequently.
The Zeroth Law is the basis of thermometry. The thermometer is system C that is in equilibrium with both A and B. This is why the temperature reading is valid — it is the exact same as the temperature of whatever the thermometer is placed in physical contact with.
$C_{p} - C_{v} = R$ (Mayer's relation) always holds for an ideal gas. $C_{p} > C_{v}$ always, because at constant pressure, extra thermal energy is needed to do the physical work of expansion ( $P Δ V = n R Δ T$ per mole). At constant volume, all heat goes directly into raising internal energy.

Practice Questions

Q1 (NEET MCQ): Which of the following is a state function?

A) Heat
B) Work
C) Internal energy
D) Both A and B

Answer: C) Internal energy.

Explanation: Heat and work are path functions — their values depend on the specific path/process taken. Internal energy ( $U$ ) is a state function — it depends only on the thermodynamic state (for an ideal gas, only on its current temperature).

Q2 (JEE Main / NEET): For a monatomic ideal gas, what is the ratio of specific heats $γ = C_{p} / C_{v}$ ?

Explanation:

A monatomic gas has exactly 3 translational degrees of freedom.
$C_{v} = \frac{3}{2} R$
$C_{p} = C_{v} + R = \frac{5}{2} R$

$γ = \frac{C_{p}}{C_{v}} = \frac{5 / 2}{3 / 2} = \frac{5}{3} \approx 1.67$

Q3 (Board): State and explain the significance of the Zeroth Law of Thermodynamics.

Explanation:

Statement: If systems A and B are each in thermal equilibrium with a third system C, then A and B are in thermal equilibrium with each other.

Significance: It establishes that temperature is a well-defined, measurable property. It provides the logical foundation for the use of thermometers — a thermometer (system C) is placed in contact with two bodies; if both give the same reading, the bodies are in thermal equilibrium with each other. Without the Zeroth Law, the concept of temperature measurement would lack a logical, scientific basis.

Q4 (JEE Main): 1 mole of an ideal diatomic gas is heated at constant pressure from 300 K to 400 K. Find the heat supplied and the increase in internal energy. ( $R = 8.314 {J mol}^{- 1} K^{- 1}$ )

Explanation:

For a diatomic gas: $C_{v} = \frac{5}{2} R$ and $C_{p} = \frac{7}{2} R$
Given $Δ T = 100 K$ and $n = 1 mole$ .

Heat supplied ( $Q$ ):
$Q = n C_{p} Δ T = 1 \times \frac{7}{2} \times 8.314 \times 100$
$= 2909.9 J$

Change in internal energy ( $Δ U$ ):
$Δ U = n C_{v} Δ T = 1 \times \frac{5}{2} \times 8.314 \times 100$
$= 2078.5 J$

(Verification: Work done $W = Q - Δ U = 2909.9 - 2078.5$
$= 831.4 J$ , which exactly matches $n R Δ T$ )

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DifficultyIntermediate

Est. Read Time24 minutes

CategoryThermodynamics

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Thermodynamic Systems, Zeroth Law & Heat

1. Basic Terminology

2. Zeroth Law of Thermodynamics

3. Heat, Work, and Internal Energy — Key Distinctions

Internal Energy ( $U$ )

Heat ( $Q$ ) and Work ( $W$ ) — Path Functions

Work Done in Thermodynamic Processes

4. Molar Heat Capacities

State Function vs Path Function — Never Confuse Again

Practice Questions

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Practice Questions

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Target Subjects

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Subject Mastery

Thermodynamic Systems, Zeroth Law & Heat

1. Basic Terminology

2. Zeroth Law of Thermodynamics

3. Heat, Work, and Internal Energy — Key Distinctions

Internal Energy (U)

Heat (Q) and Work (W) — Path Functions

Work Done in Thermodynamic Processes

4. Molar Heat Capacities

State Function vs Path Function — Never Confuse Again

Practice Questions

Related Study Material

Practice Questions

Topic Information

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Internal Energy ( $U$ )

Heat ( $Q$ ) and Work ( $W$ ) — Path Functions