NDA Physics · Heat and Thermodynamics

Heat, Specific Heat, Calorimetry, and Heat Transfer

Heat is energy in transit driven by a temperature difference; specific heat sets how much heat a unit mass needs per degree, calorimetry balances heat lost against heat gained, and heat moves by conduction, convection, or radiation.

All Heat and Thermodynamics notes NDA Physics strategy

Why this matters

This is the chapter's biggest marks pool — about 12 PYQs and the home of every HARD calorimetry numeric. The recall layer is steady (heat is energy transfer due to a temperature difference; specific heat is a material property; thermal capacity = mass × specific heat). The HARD layer is the ice-melting mixing problem: you set heat gained = heat lost, remembering to include the latent-heat term while ice melts at constant temperature. The three modes of heat transfer (conduction, convection, radiation) are a near-guaranteed one-mark recall — the thermos-flask question lives here too.

Concept 1 of 5

Heat — energy in transit due to a temperature difference

Intuition

Heat is NOT something a body 'contains' — it is energy that FLOWS from a hotter body to a colder one because of the temperature difference between them. The moment they reach the same temperature, the flow stops. Energy can also be transferred by doing work, but that is not heat; heat specifically means transfer driven by a temperature difference.

Definition

Heat is the energy transferred between bodies (or a body and its surroundings) because of a temperature difference. Key consequences:

Heat always flows from higher temperature to lower temperature on its own.
Any energy transfer NOT driven by a temperature difference (e.g. mechanical work) is not heat.
Heat is measured in joules (J); an older unit is the calorie (1 cal = 4.18 J), where 1 calorie raises 1 g of water by 1°C.

Worked example

Two blocks at 80°C and 30°C are placed in contact and isolated. In which direction does heat flow, and when does it stop?

Heat flows from the hotter body to the colder body — from the 80°C block to the 30°C block.
It keeps flowing as long as a temperature difference exists.
It stops when both reach a common (equilibrium) temperature somewhere between 30°C and 80°C.

Answer:From the 80°C block to the 30°C block, until they reach the same temperature.

Practice this conceptself-check · 4 quick reps

Try it yourself

Which statement best defines heat: (i) energy a body stores, or (ii) energy transferred due to a temperature difference?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
Heat flows from a body at higher temperature to one at lower temperature: true or false?
2.
Is mechanical work a form of heat?
3.
1 calorie raises the temperature of 1 g of water by how much?
4.
The SI unit of heat is?

From the bank · past-year question

Example 1Heat and ThermodynamicsEASY

Which one of the following statements best defines the concept of heat ?

[Q94 · Sep · 2024]

A body has internal energy, not 'heat'

It is loose to say a hot body 'has a lot of heat'. Strictly, heat is energy IN TRANSIT — once absorbed it becomes the body's internal energy. NDA tests the precise definition: energy transferred due to a temperature difference.

Drill 1 more on heat — energy in transit due to a temperature difference

Concept 2 of 5

Specific heat, thermal capacity, and Q = mcΔT

Intuition

Different substances need different amounts of heat to warm up by the same amount. Specific heat capacity is how much heat one kilogram of a substance needs to rise by one degree — water's is famously high, which is why the sea moderates climate. Multiply specific heat by mass and you get the body's thermal (heat) capacity: how much heat it needs per degree as a whole object.

Definition

Specific heat capacity $c$ : heat needed to raise the temperature of unit mass (1 kg) of a substance by 1°C (or 1 K). It is an intrinsic material property — independent of the mass and shape of the body. Thermal (heat) capacity $= mc$ : heat needed to raise the WHOLE body by 1°C. It depends on mass (for a given material) but not on shape. The heat to change a body's temperature is $Q = mc\,\Delta\theta$ .

Sensible heat (no phase change)

Q = mc\,\Delta\theta \qquad \text{Thermal capacity} = mc

Qheat supplied or removed (J)
mmass (kg)
cspecific heat capacity (J/(kg·°C))
\Delta\thetachange in temperature (°C or K)

Worked example

How much heat is needed to raise the temperature of 3 kg of copper (specific heat

390\,\text{J/(kg·°C)}

) from 25°C to 75°C?

Temperature rise: $\Delta\theta = 75 - 25 = 50°\text{C}$ .
Apply $Q = mc\,\Delta\theta = 3 \times 390 \times 50$ .
$Q = 1170 \times 50 = 58500\,\text{J}$ , i.e. 58.5 kJ.

Answer:58 500 J (58.5 kJ).

Practice this conceptself-check · 4 quick reps

Try it yourself

On what does the thermal (heat) capacity of a body depend — mass, shape, both, or temperature?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
Specific heat depends on mass and shape: true or false?
2.
Heat to warm 2 kg of water (c = 4200) by 5°C?
3.
Thermal capacity = mass × ?
4.
Which has higher specific heat — water or iron?

From the bank · past-year question

Example 2Heat and ThermodynamicsEASY

What is the mass of a material, whose specific heat capacity is

400 \, \text{J/(kg °C)}

for a rise in temperature from

15\,°C

25\,°C

, when heat received is

20 \, \text{kJ}

[Q51 · Apr · 2022]

Specific heat is intrinsic; thermal capacity is not

Specific heat capacity does NOT depend on mass or shape — it is the same for 1 g or 1 tonne of the material. Thermal capacity

= mc

DOES scale with mass. The NDA repeatedly tests this distinction (statements like 'specific heat depends on mass' are false).

Watch the units — kJ vs J, kg vs g

Convert kilojoules to joules and grams to kilograms before plugging in, or the answer is off by a factor of 1000. In

Q = mc\,\Delta\theta

keep

c

in J/(kg·°C) with

m

in kg.

Drill 3 more on specific heat, thermal capacity, and q = mcδt

Concept 3 of 5

Latent heat and the calorimetry mixing balance

Intuition

When a substance changes phase — ice to water, water to steam — it absorbs heat WITHOUT changing temperature. That hidden heat is the latent heat. In a mixing problem you must account for it separately from the warming/cooling heat. The master principle is conservation of energy: in an isolated mix, heat lost by the hot bodies equals heat gained by the cold ones.

Definition

Latent heat $L$ : heat per unit mass absorbed or released during a phase change at constant temperature — $Q = mL$ . For water (in calorie units): latent heat of fusion (melting) $\approx 80$ cal/g; latent heat of vaporization $\approx 540$ cal/g. Principle of calorimetry (method of mixtures): in an isolated system,

Heat lost by hot bodies = heat gained by cold bodies.
A calorimetry problem chains $Q = mc\,\Delta\theta$ terms (temperature change) with $Q = mL$ terms (phase change) until everything reaches a common final temperature.

Latent heat + the mixing balance

Q = mL \qquad \sum Q_{\text{lost}} = \sum Q_{\text{gained}}

Lspecific latent heat (cal/g or J/kg)
mmass undergoing phase change
Qheat absorbed/released at constant temperature

Worked example

5 g of ice at −20°C is dropped into m kg of water at 30°C. The final state is liquid at 0°C. Find m. (Take ice specific heat 0.5 cal/(g·°C), latent heat of fusion 80 cal/g, water specific heat 1 cal/(g·°C).)

Heat GAINED by ice (cold body): warm ice from −20°C to 0°C, then melt it at 0°C.
Warming: $5\times 0.5\times 20 = 50$ cal. Melting: $5\times 80 = 400$ cal. Total gained $= 450$ cal.
Heat LOST by water (hot body) cooling from 30°C to 0°C: $(m\times 1000)\times 1\times 30$ cal (mass in grams = $1000m$ ).
Balance: $1000m\times 30 = 450 \Rightarrow m = \frac{450}{30000} = 0.015\,\text{kg}$ .

Answer:m = 0.015 kg (15 g).

Practice this conceptself-check · 4 quick reps

Try it yourself

10 g of ice at −10°C is mixed with 10 g of water at 0°C. How much heat is needed to raise the whole mixture to 10°C? (ice c = 0.5, fusion 80, water c = 1, all cal/g.)

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
Heat to melt 4 g of ice at 0°C (L = 80 cal/g)?
2.
During melting, does the temperature change?
3.
State the calorimetry balance in words.
4.
Latent heat of vaporization of water (cal/g)?

From the bank · past-year question

Example 3Heat and ThermodynamicsHARD

A 5 g piece of ice at

-20\,°C

is put into

m

kg of water at

30\,°C

. The final temperature is

0\,°C

in liquid phase. What is the value of

m

in kg?

[Q61 · Apr · 2026]

Don't forget the latent-heat term while ice is melting

A classic error is treating ice → water as pure

Q = mc\,\Delta\theta

. The melting itself absorbs

mL

at a flat 0°C with no temperature change. Add a separate

mL

term, or your heat budget is hundreds of calories short.

Keep masses in consistent units across both sides

In these problems one mass is in grams (ice) and the other may be given in kg (water). Convert to grams everywhere (or kg everywhere) before equating heat lost and heat gained.

Drill 1 more on latent heat and the calorimetry mixing balance

Concept 4 of 5

When specific heat varies with temperature

Intuition

If a material's specific heat changes with temperature — say

C(T) = C_0 + \alpha T

— you cannot just use

Q = mc\,\Delta\theta

with a single

c

. Instead you add up

mC(T)\,dT

over the temperature range, which means integrating.

Definition

When specific heat is temperature-dependent, the heat supplied is the integral

Q = m\int_{T_1}^{T_2} C(T)\,dT.

For the common linear form

C(T) = C_0 + \alpha T

, this evaluates to

Q = m(T_2 - T_1)\left[C_0 + \tfrac{1}{2}\alpha(T_1 + T_2)\right],

i.e. the bracket carries the average value of

C

over the interval.

Heat for a temperature-dependent specific heat

Q = m\int_{T_1}^{T_2}\!\big(C_0 + \alpha T\big)\,dT = m(T_2 - T_1)\left[C_0 + \tfrac{1}{2}\alpha(T_1 + T_2)\right]

C_0specific heat at T = 0 (a constant)
\alpharate of change of specific heat with temperature
T_1, T_2initial and final temperatures

Worked example

A solid of mass m has specific heat

C(T) = C_0 + \alpha T

. It is heated from

T_1

T_2

. Find the heat Q supplied.

Write $Q = m\int_{T_1}^{T_2}(C_0 + \alpha T)\,dT$ .
Integrate: $\int(C_0 + \alpha T)\,dT = C_0 T + \tfrac{\alpha}{2}T^2$ .
Evaluate: $Q = m\left[C_0(T_2 - T_1) + \tfrac{\alpha}{2}(T_2^2 - T_1^2)\right]$ .
Factor $(T_2 - T_1)$ using $T_2^2 - T_1^2 = (T_2 - T_1)(T_2 + T_1)$ : $Q = m(T_2 - T_1)\left[C_0 + \tfrac{\alpha}{2}(T_1 + T_2)\right]$ .

Answer:

Q = m(T_2 - T_1)\left[C_0 + \tfrac{1}{2}\alpha(T_1 + T_2)\right]

Practice this conceptself-check · 3 quick reps

Try it yourself

A 2 kg solid has

C(T) = 100 + 0.2T

(SI). Find the heat to warm it from

T_1 = 100\,\text{K}

T_2 = 200\,\text{K}

Practice — Level 1 (3 reps)

Quick reps to lock in the method. Try each, then check.

1.
For variable c, Q equals the integral of what?
2.
The bracket $C_0 + \tfrac{1}{2}\alpha(T_1+T_2)$ represents what?
3.
$\int(C_0 + \alpha T)\,dT = ?$

From the bank · past-year question

Example 4Heat and ThermodynamicsHARD

A solid of mass

m

has temperature-dependent specific heat

C(T) = C_0 + \alpha T

, where

C_0

and

\alpha

are constants. The solid is heated from

T_1

T_2

. Which one of the following is the correct expression for heat

Q

[Q53 · Apr · 2026]

The factor on $\alpha$ is one-half, not one

The planted distractor uses

[C_0 + \alpha(T_1 + T_2)]

(no one-half). The integral of

\alpha T

gives

\tfrac{\alpha}{2}T^2

, so after factoring you get

\tfrac{1}{2}\alpha(T_1 + T_2)

— the half is essential.

Concept 5 of 5

The three modes of heat transfer — conduction, convection, radiation

Intuition

Heat moves from hot to cold in exactly three ways. CONDUCTION passes heat molecule-to-molecule through a solid without the molecules travelling. CONVECTION carries heat by the bulk movement of a heated fluid (warm fluid rises, cool sinks). RADIATION sends heat as electromagnetic waves — it needs no medium and travels at the speed of light, which is how the Sun warms the Earth across empty space.

Definition

Three independent mechanisms by which heat is transferred. The defining facts that the NDA tests: conduction needs contact and no bulk motion, convection needs a moving fluid, and radiation needs no medium and travels at the speed of light.

Conduction and convection both require matter to carry the heat; only radiation crosses a vacuum, which is how the Sun warms the Earth.

Mode	How it works	Medium / key fact
Conduction	Heat passes molecule to molecule; molecules vibrate in place and pass energy to neighbours without moving from their positions	Needs a material medium; dominant in solids (especially metals)
Convection	Heated fluid becomes less dense and rises; cooler fluid sinks to replace it, setting up a circulating current that carries heat	Needs a fluid (liquid or gas) that can flow; bulk movement of matter
Radiation	Heat travels as electromagnetic (infrared) waves in a straight line	Needs NO medium; travels at the speed of light — how the Sun heats Earth NDA 2019 — 'heat waves travel in a straight line with the speed of light' is THERMAL RADIATION (not conduction or convection).

Conduction and convection both require a medium; only radiation crosses vacuum. A thermos flask defeats all three: vacuum gap stops conduction/convection, silvered walls reflect radiation.

Practice this conceptself-check · 5 quick reps

Try it yourself

Which one of these statements about a thermos (vacuum) flask is NOT correct? (a) the walls are separated by vacuum, (b) the glass walls have shiny silvered surfaces, (c) the inner wall radiates heat and the outer wall absorbs it, (d) the cork supports are poor conductors.

Practice — Level 1 (5 reps)

Quick reps to lock in the method. Try each, then check.

1.
Which mode of heat transfer needs no medium?
2.
Heat transfer through a metal rod is by which mode?
3.
How does heat travel through boiling water (a fluid)?
4.
Radiation travels at the speed of what?
5.
What stops conduction and convection in a thermos flask?

From the bank · past-year question

Example 5Heat and ThermodynamicsEASY

In which of the following phenomena do heat waves travel along a straight line with the speed of light?

[Q53 · Sep · 2019]

Only radiation crosses a vacuum

Conduction and convection BOTH need matter — conduction needs contact, convection needs a flowing fluid. Radiation alone needs no medium, which is why the Sun's heat reaches us through the vacuum of space. Any 'heat travels at the speed of light' clue means radiation.

A thermos REFLECTS radiation — it does not absorb it

The silvered walls are there to reflect infrared back, not to soak it up. An option saying the inner wall radiates and the outer absorbs is the planted wrong statement on 'which is NOT correct' questions.

Drill 1 more on the three modes of heat transfer — conduction, convection, radiation

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Specific heat, thermal capacity, and Q = mcΔT
Sensible heat (no phase change)
$Q = mc\,\Delta\theta \qquad \text{Thermal capacity} = mc$
Latent heat and the calorimetry mixing balance
Latent heat + the mixing balance
$Q = mL \qquad \sum Q_{\text{lost}} = \sum Q_{\text{gained}}$
When specific heat varies with temperature
Heat for a temperature-dependent specific heat
$Q = m\int_{T_1}^{T_2}\!\big(C_0 + \alpha T\big)\,dT = m(T_2 - T_1)\left[C_0 + \tfrac{1}{2}\alpha(T_1 + T_2)\right]$

Reference tables (1)

The three modes of heat transfer — conduction, convection, radiation3 rows

Mode	How it works	Medium / key fact
Conduction	Heat passes molecule to molecule; molecules vibrate in place and pass energy to neighbours without moving from their positions	Needs a material medium; dominant in solids (especially metals)
Convection	Heated fluid becomes less dense and rises; cooler fluid sinks to replace it, setting up a circulating current that carries heat	Needs a fluid (liquid or gas) that can flow; bulk movement of matter
Radiation	Heat travels as electromagnetic (infrared) waves in a straight line	Needs NO medium; travels at the speed of light — how the Sun heats Earth NDA 2019 — 'heat waves travel in a straight line with the speed of light' is THERMAL RADIATION (not conduction or convection).

Conduction and convection both require a medium; only radiation crosses vacuum. A thermos flask defeats all three: vacuum gap stops conduction/convection, silvered walls reflect radiation.

Watch out for (8)

A body has internal energy, not 'heat'
→ Heat — energy in transit due to a temperature difference
Specific heat is intrinsic; thermal capacity is not
→ Specific heat, thermal capacity, and Q = mcΔT
Watch the units — kJ vs J, kg vs g
→ Specific heat, thermal capacity, and Q = mcΔT
Don't forget the latent-heat term while ice is melting
→ Latent heat and the calorimetry mixing balance
Keep masses in consistent units across both sides
→ Latent heat and the calorimetry mixing balance
The factor on $\alpha$ is one-half, not one
→ When specific heat varies with temperature
Only radiation crosses a vacuum
→ The three modes of heat transfer — conduction, convection, radiation
A thermos REFLECTS radiation — it does not absorb it
→ The three modes of heat transfer — conduction, convection, radiation

Mastery check — 5 interleaved questions

Try each one before clicking. Questions are interleaved across the concepts above, not grouped — interleaving sharpens transfer.

Example 1Heat and ThermodynamicsMODERATE

Which one of the following statements is correct?

[Q51 · Apr · 2018]

Example 2Heat and ThermodynamicsHARD

Which of the following statements about specific heat of a body is/are correct? 1. It depends upon mass and shape of the body. 2. It is independent of mass and shape of the body. 3. It depends only upon the temperature of the body. Select the correct answer using the code given below:

[Q101 · Apr · 2018]

Example 3Heat and ThermodynamicsHARD

10 g of ice at

-10°\text{C}

is mixed with 10 g of water at 0°C. The amount of heat required to raise the temperature of mixture to 10°C is

[Q72 · Sep · 2019]

Example 4Heat and ThermodynamicsMODERATE

Which one of the following statements regarding a thermos flask is NOT correct?

[Q115 · Apr · 2019]

Example 5Heat and ThermodynamicsMODERATE

Which one of the following statements is NOT correct ?

[Q82 · Apr · 2017]

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