Heat & Thermodynamics – NDA Physics Notes

Hold a hot cup of tea. Within seconds you feel the warmth in your hands. Leave it on the table and it cools gradually, eventually reaching room temperature.

This simple everyday experience encodes the entire subject of heat and thermodynamics. Heat is energy flowing because of a temperature difference. Thermodynamics is the science that governs every aspect of that flow: how it occurs, how fast it occurs, which direction it must go, and the absolute limits on what can be accomplished with it.

From temperature measurement to steam engines, from the greenhouse effect to the freezing of lakes, the concepts in this chapter govern the physical world from everyday kitchen physics to the foundations of industrial civilization.

1. What Is Heat?

In everyday language, heat means warmth. In Physics, heat has a precise definition that is narrower and more powerful.

Heat is the transfer of energy from one body to another due to a temperature difference. [NDA 2024-II | NDA 2018-I] The direction of that transit: always from higher temperature to lower temperature.

Heat is NOT: a transformation of energy from one form to another in general. That is the broader concept of energy conversion.

Heat is NOT: a change in volume with temperature. That is thermal expansion.

Heat IS: specifically, energy in transit across a temperature difference.

Adiabatic Systems

A system that does not allow exchange of heat with its surroundings is called an adiabatic system. [NDA 2025-I] In an adiabatic process, Q = 0. The First Law gives ΔU = −W.

2. Temperature Scales

Temperature measures how hot or cold something is, or equivalently, the average kinetic energy of the molecules in a substance. Three scales are used in Physics.

Scale	Freezing Point of Water	Boiling Point of Water	Absolute Zero	Degree Size
Celsius (°C)	0°C	100°C	−273.15°C	Same as Kelvin
Fahrenheit (°F)	32°F	212°F	−459.67°F	Smallest (5/9 of Celsius)
Kelvin (K)	273.15 K	373.15 K	0 K	Same as Celsius

3. Converting Between Temperature Scales

The three essential conversion formulas:

°F = 32 + (9/5) × °C  =  32 + 1.8 × °C

K  = °C + 273.15   (use 273 for NDA calculations)

°C = (°F − 32) × 5/9  =  (°F − 32) / 1.8

The constant X in °F = X + 1.8 × °C is 32. [NDA 2019-I]

Five NDA-Tested Conversion Patterns

Pattern 1 : Fahrenheit to Kelvin (113°F → 318 K):

Step 1: °C = (113 − 32) / 1.8 = 81/1.8 = 45°C

Step 2: K = 45 + 273 = 318 K   [NDA 2019-II]

Pattern 2 : Kelvin rise = Celsius rise: A temperature increase of 30 K equals exactly 30°C : only zero points differ. [NDA 2025-II]

Pattern 3 : Fahrenheit = Celsius at −40°:

Setting °F = °C: °C = 32 + 1.8°C → −0.8°C = 32 → °C = −40°   [NDA 2021-I]

Pattern 4 : K = F numerically when Celsius ≈ 301°C:

Setting K = F: (°C + 273) = (32 + 1.8°C) → 241 = 0.8°C → °C ≈ 301°C   [NDA 2017-I]

Pattern 5 : Absolute zero in Celsius:

0 K = 0 − 273 = −273°C   [NDA 2015-II | NDA 2018-II | NDA 2021-I]

4. Special Temperature Values

Absolute zero = 0 K = −273.15°C ≈ −273°C. It is the lowest possible temperature. Temperature below absolute zero is physically impossible. The Kelvin scale has no negative values.

Degree Interval Comparison: The Fahrenheit degree is the smallest interval among common scales. [NDA 2010-I] Between freezing and boiling: Celsius covers 100 degrees, Fahrenheit covers 180 degrees. Celsius = Kelvin in interval size. Order: Fahrenheit < Celsius = Kelvin.

5. Thermometer Types and Their Limits

Thermometer Type	Lower Limit	Upper Limit	Why Limited	NDA Application
Mercury	−38.8°C (mercury freezes)	357°C (mercury boils)	Mercury phase change	Cannot measure −250°C
Alcohol	−114°C (alcohol freezes)	78°C (alcohol boils)	Alcohol phase change	Cannot measure very high T
Clinical (mercury)	35°C	42°C	Designed only for body temperature range	Very limited range
Thermocouple	Near absolute zero	Several thousand °C	Electrical measurement : no phase change limit	ONLY valid for −250°C

For measuring −250°C, only a thermocouple thermometer is suitable. Mercury freezes at −38.8°C. [NDA 2025-II]

6. Specific Heat Capacity

Different materials absorb different amounts of heat for the same temperature change. This is captured by specific heat capacity (c), the heat required to raise unit mass by 1°C. It is a material property, independent of mass and shape. [NDA 2018-I]

Q = mcΔT

Q = heat (J). m = mass (kg). c = specific heat (J kg⁻¹ K⁻¹). ΔT = temperature change (°C or K).

Specific Heat Is Mass-Independent

Body A (2 kg) and body B (4 kg) same material, same conditions: B absorbs exactly double the heat, because double mass with same c and ΔT. [NDA 2012-I]

Finding Mass from Heat

Q = 20 kJ, c = 400 J/(kg°C), ΔT = 10°C.

m = Q/(cΔT) = 20,000 / (400 × 10) = 5 kg   [NDA 2022-I]

7. Thermal Capacity

Thermal capacity of a body = heat required to raise the entire body by 1°C.

Thermal capacity = m × c   (SI unit: J K⁻¹)

Thermal capacity depends on mass. Specific heat (c) does NOT depend on mass. [NDA 2018-I]

Property	Specific Heat Capacity (c)	Thermal Capacity
Definition	Heat per unit mass per degree	Heat per degree for whole body
Formula	c = Q/(mΔT)	C = mc
SI unit	J kg⁻¹ K⁻¹	J K⁻¹
Depends on mass?	NO : material property	YES : mass × specific heat
Larger body same material?	Same c	Larger C (more mass)

8. Latent Heat

When a substance changes phase, it absorbs or releases heat without any change in temperature. This energy is called latent heat (hidden heat).

On the θ-Q graph, the horizontal (flat) segments represent latent heat, as temperature is constant during phase change. [NDA 2012-I]

Specific Latent Heat of Vaporisation: Heat required to convert unit mass of liquid to vapour at constant temperature (no temperature rise). [NDA 2022-I | NDA 2025-II | NDA 2017-I]

Why Water at 0°C Does Not Immediately Freeze: Water at 0°C must release its latent heat of fusion before it can freeze. Heat must be removed, not supplied. Reaching 0°C is only the temperature threshold. [NDA 2012-I]

Cooling Curve: During cooling of a liquid, the temperature-time graph shows a horizontal plateau at the freezing point, as latent heat is released at constant temperature. [NDA 2015-I]

Evaporation Cools the Body: Perspiration cools the body because evaporation of sweat requires latent heat drawn from the body surface. [NDA 2015-I] A fan accelerates evaporation through air movement, not by supplying cool air. [NDA 2010-I] Evaporation is faster when: temperature is high AND surface area is large. [NDA 2022-I]

9. Calorimetry : Mixing Calculations

When two substances at different temperatures are mixed in an insulated container: Heat lost by hotter body = Heat gained by cooler body.

Ice-Water Mixing : NDA 2026-I

5 g ice at −20°C mixed with m kg water at 30°C. Final temperature = 0°C. c_ice = 2100 J/(kg°C), L = 3.36×10⁵ J/kg, c_water = 4200 J/(kg°C).

Heat gained by ice: Q₁ = (0.005)(2100)(20) = 210 J    (warming −20°C → 0°C)

                   Q₂ = (0.005)(3.36×10⁵) = 1680 J  (melting)

Total Q_ice = 210 + 1680 = 1890 J

Heat lost by water: Q₃ = m(4200)(30) = 126,000m J

126,000m = 1890  →  m = 0.015 kg   [NDA 2026-I]

10. Thermal Expansion

When a solid is heated, its atoms vibrate more vigorously, pushing neighbours apart. The solid expands in every dimension.

Effect on a Pendulum Clock: T = 2π√(L/g). Heating increases wire length L → period T increases slightly → clock runs slow. [NDA 2017-I]

Why Liquid Expansion Is Hard to Measure: The container also expands. What is measured directly is only apparent expansion. Real expansion = apparent + container expansion. [NDA 2017-I]

11. Thermal Expansion Coefficients

β (areal)      = 2α (linear)

γ (volumetric) = 3α = (3/2)β

Logic: Area = 2D → 2α. Volume = 3D → 3α.

Worked Example: β = 1.6×10⁻⁵ K⁻¹ → γ = (3/2)(1.6×10⁻⁵) = 2.4×10⁻⁵ K⁻¹.   [NDA 2018-II]

12. Anomalous Expansion of Water

Water contracts as it cools from 100°C to 4°C (normal). But between 4°C and 0°C, water expands as it cools. Density decreases. Water is densest at 4°C.

The incorrect statement: “as ice melts it expands uniformly up to 4°C”: this is FALSE. Water contracts (density increases) from 0°C to 4°C. [NDA 2016-I]

Why Lakes Freeze from the Top: Cooling surface water sinks until 4°C (densest). Below 4°C, water expands and floats. Surface freezes at 0°C while bottom stays at 4°C. Fish survive. [NDA 2014-I]

13. Modes of Heat Transfer: Overview

Property	Conduction	Convection	Radiation
Mechanism	Molecular vibration: molecule to molecule	Bulk movement of fluid	Electromagnetic waves (infrared)
Medium required?	Yes: solid medium	Yes: fluid (liquid or gas)	No: travels in vacuum
Molecules move?	No: vibrate in place	Yes: bulk fluid movement	No medium needed
Best in	Solids (metals)	Liquids and gases	Vacuum and all media
Speed	Slow	Moderate (fluid currents)	Speed of light
Examples	Silver best; rods in series	Trade winds; water heating	Sun to Earth; thermos

14. Conduction

In conduction, energy passes molecule-to-molecule via vibration. Molecules do not move from place to place.

Best and Poorest Conductors

Best: Silver (Ag). Poorest metallic: Lead (Pb). [NDA 2010-I] Order: silver > copper > gold > aluminium > steel > lead. Order among common materials: steel > water > wood. [NDA 2012-II]

SI Unit of Thermal Conductivity

SI unit: W m⁻¹ K⁻¹ (watts per metre per kelvin). [NDA 2015-II]

Junction Temperature: Two Rods in Series

Copper (k=4, cold end 0°C) and brass (k=1, hot end 100°C) are joined. Heat flow rate equal through both:

4(T_j − 0) = 1(100 − T_j)  →  4T_j = 100 − T_j  →  T_j = 20°C   [NDA 2012-I]

Junction is closer to 0°C end because copper (better conductor) needs smaller temperature gradient.

15. Convection

In convection, heat is transferred by bulk movement of a fluid. Hot fluid rises (less dense), cool fluid sinks (denser), forming convection currents.

Trade Winds : Global Convection: Air above equator heats up, rises (low pressure at equator). Cooler air flows in from higher latitudes : these are the trade winds. [NDA 2011-II]

16. Radiation

In radiation, heat is transferred by electromagnetic waves (infrared). Radiation requires no medium. It travels through vacuum. [NDA 2019-II] Travels at the speed of light.

Absorption and Emission by Surfaces

Dark (black) surfaces: better absorbers AND better emitters than light (silver) surfaces. Dark skin: more heat in sunshine (absorbs more) AND more cold in cold (emits more). Both effects amplified. [NDA 2010-I]

This relationship (good absorber = good emitter) is Kirchhoff’s Law of Radiation.

Rate of Radiation Loss

Depends on temperature difference between body and surroundings (Stefan’s Law: E = σT⁴). [NDA 2012-II]

17. The Thermos Flask: All Three Modes Minimised

Mode	How the Thermos Minimises It
Conduction	Vacuum between double glass walls: nothing to conduct through.
Convection	Vacuum has no molecules: convection impossible.
Radiation	Silvered inner surfaces: silver is a poor emitter and poor absorber. Radiation reflected back.

The incorrect statement: “inner wall radiates a good amount of heat.” [NDA 2019-I] The silvered inner wall is a poor emitter. It reflects radiation back rather than emitting it.

18. Greenhouse Effect

Sun emits short-wavelength visible radiation that passes through atmosphere. Earth re-emits as long-wavelength infrared. Greenhouse gases (CO₂, CH₄, N₂O, H₂O) absorb outgoing infrared and re-radiate some back, trapping heat. [NDA 2015-I]

Greenhouse gases do not emit heat themselves. They intercept outgoing infrared from Earth’s surface and redirect some back downward.

19. Newton’s Law of Cooling

The rate of cooling is proportional to the excess temperature above surroundings (when that excess is small):

dT/dt ∝ −(T − T_surroundings)

Applies only when: (i) body temperature is changing, (ii) temperature excess above surroundings is small, (iii) surroundings at constant temperature.

Situation	Temp Changing?	Small Excess?	Applies?
Ice melting in water	NO: stays at 0°C	—	NO
Water boiling in an open container	NO: stays at 100°C	—	NO
Metal rod in furnace	YES but large difference	NO	NO
Cup of coffee cooling on a table	YES: gradual	YES	YES

Only a cup of coffee cooling on a table satisfies Newton’s Law of Cooling conditions. [NDA 2024-II]

20. Laws of Thermodynamics

Zeroth Law

If A is in thermal equilibrium with B, and B with C, then A is in thermal equilibrium with C. This defines temperature.

First Law

ΔU = Q − W

ΔU = change in internal energy. Q = heat added. W = work done by system. When W = 0: ΔU = Q. [NDA 2019-II]

Second Law

Heat cannot spontaneously flow from a colder body to a hotter body. [NDA 2017-II] A heat engine cannot convert all heat to work. Some must be rejected to a cold reservoir.

Adiabatic Systems

Q = 0 → ΔU = −W. [NDA 2025-I]

21. Ideal Gas Laws

Boyle’s Law: Isothermal Process

PV = constant   (constant temperature)

If pressure doubles, volume halves.

The 10% Pressure Confusion

Pressure increases 10% (P → 1.1P). V_new = PV/(1.1P) = V/1.1 ≈ 0.909V. Volume decreases by 9.1%, not 10%. [NDA 2014-I] The relationship is multiplicative, not additive.

V vs 1/P Graph

V = const × (1/P). V vs 1/P: straight line through origin. V vs P: hyperbola. [NDA 2016-II]

Melting Point and Intermolecular Forces

Melting point indicates strength of intermolecular attractive forces. [NDA 2016-I] Iron melts at approximately 1500°C. [NDA 2019-I]

22. Thermodynamic Processes

Process	Constant	PV Relationship	Heat Q	Work W	ΔU
Isothermal	Temperature T	PV = const (hyperbola)	Q = W	nRT ln(V₂/V₁)	0
Adiabatic	Q = 0	PVᵞ = const (steeper)	0	−ΔU	−W
Isochoric	Volume V	P/T = const	Q = nCᵥΔT	0	Q
Isobaric	Pressure P	V/T = const	Q = nCₚΔT	PΔV	Q − W

Polytropic: PV² = constant

PV² = const and PV = nRT → TV = constant → T₁/T₂ = V₂/V₁. [NDA 2026-I]

Process P = kT : Identifying the Heat Capacity

P = kT. From PV = nRT: (kT)V = nRT → kV = nR → V = constant. This is an isochoric (constant volume) process → C = Cᵥ. [NDA 2026-I]

23. Carnot Cycle and Efficiency

A heat engine absorbs heat Q_h from a hot reservoir (temperature T_h), converts some to work W, rejects waste heat Q_c to cold reservoir (temperature T_c).

η_Carnot = 1 − T_c/T_h   (temperatures in Kelvin)

Always η < 1 (less than 100%) because T_c/T_h > 0 for any real temperatures. No engine can be 100% efficient. This is a Second Law consequence.

Example: T_h = 500 K, T_c = 300 K. η = 1 − 300/500 = 40%. The engine converts 40% of absorbed heat into work.

24. Advanced Thermal Applications

Temperature-Dependent Specific Heat [NDA 2026-I]

For solid with C(T) = C₀ + αT, heated from T₁ to T₂:

Q = m∫[T₁ to T₂](C₀ + αT)dT = m(T₂−T₁)[C₀ + (α/2)(T₁+T₂)]

The effective average specific heat = C₀ + (α/2)(T₁ + T₂).   [NDA 2026-I]

Speed of Sound and Pressure (NDA 2026-I)

v = √(γP/ρ). At constant temperature, ρ ∝ P so P/ρ = RT/M = constant. Speed of sound is independent of pressure at constant temperature. [NDA 2026-I]

Stefan-Boltzmann Law

E = σT⁴   (σ = 5.67×10⁻⁸ W m⁻² K⁻⁴)

Power radiated ∝ T⁴. Doubling temperature increases radiation 16-fold.

Entropy

Entropy measures disorder/randomness. Second Law restated: in any spontaneous process, total entropy of universe increases.

Important Distinctions

Heat vs Temperature

Heat = energy in transit (Joules). Temperature = average molecular kinetic energy (K or °C). Heat flows because of temperature differences.

Specific Heat vs Thermal Capacity

Specific heat: material property, mass-independent. Thermal capacity = mc: depends on mass. Same material, double mass → same c, double thermal capacity.

Latent Heat vs Sensible Heat

Sensible heat: Q = mcΔT (temperature changes). Latent heat: Q = mL (phase changes, constant temperature). θ-Q graph: sloped = sensible; flat = latent.

Isothermal vs Adiabatic

Isothermal: constant T, ΔU = 0, PV = const (hyperbola). Adiabatic: Q = 0, temperature changes, PVᵞ = const (steeper).

Conduction vs Convection vs Radiation

Conduction: no bulk movement, needs solid. Convection: bulk fluid movement, needs fluid. Radiation: electromagnetic waves, no medium needed, speed of light.

---