Calorimetry

Q: The specific heat capacity of copper is 390 J kg-1 K-1. What is the heat capacity of a 2 kg copper block?

C' = m c = 2 × 390 = 780 J K-1.

ICSE Class 10 · Physics · Chapter 11

What this chapter covers

Heat, temperature and their units
Heat capacity
Specific heat capacity
Principle of method of mixtures
High specific heat capacity of water
Change of state and the heating curve of water
Latent heat and specific latent heat of fusion
Phenomena involving latent heat of fusion

Key definitions

Heat is the form of energy that flows from a body at a higher temperature to a body at a lower temperature when the two are in thermal contact.

Temperature is the degree of hotness or coldness of a body, and it decides the direction in which heat will flow between two bodies in contact.

Calorimetry is the branch of physics that deals with the measurement of the quantity of heat given out or taken in by a body.

The joule is the SI unit of heat, equal to the energy transferred when a force of one newton moves its point of application through one metre in the direction of the force.

One calorie is the quantity of heat required to raise the temperature of 1 g of water through 1 °C (more exactly, from 14.5 °C to 15.5 °C).

Heat capacity is the amount of heat energy required to raise the temperature of the whole of a body by 1 °C (or 1 K).

Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass (1 kg) of a substance by 1 °C (or 1 K).

Change of state is the change of a substance from one physical state (solid, liquid or gas) to another, caused by heat being supplied or removed at a fixed temperature.

The melting point is the fixed temperature at which a solid changes into its liquid state at normal atmospheric pressure.

A heating curve is a graph of the temperature of a substance against time while heat is supplied to it at a steady rate.

Latent heat is the heat energy absorbed or released by a substance during a change of state, without any change in its temperature.

Specific latent heat of fusion is the amount of heat energy required to change a unit mass (1 kg) of a solid at its melting point into liquid at the same temperature.

Key points

Heat is energy that flows from a hotter body to a colder one; temperature decides the direction of that flow.
The SI unit of heat is the joule; 1 cal ≈ 4.2 J. Temperature is measured in °C or K, with T(K) = t(^\circC) + 273, and a change of 1 °C equals a change of 1 K.
Heat capacity C' = Q/Δ T belongs to a body; its SI unit is J K^-1.
Specific heat capacity c = Q/(m Δ T) belongs to a material; its SI unit is J kg^-1 K^-1.
The two are related by C' = m c, and heat for a temperature change is Q = m c Δ T.
Values to remember: water 4200, ice 2100, copper about 390 (or 400) J kg^-1 K^-1.
Principle of method of mixtures: heat lost by the hot body = heat gained by the cold body, m₁ c₁ (T₁ - T) = m₂ c₂ (T - T₂), when no heat is lost to the surroundings.
The high specific heat capacity of water explains land and sea breezes, mild coastal climates, its use as a coolant and in hot-water bottles, and the protection of crops and aquatic life.
During a change of state the temperature stays constant; the heat taken in or given out is latent heat.
The heating curve of water has sloping parts (warming in one state) and flat parts (melting at 0 °C, boiling at 100 °C).
Specific latent heat of fusion: Q = m L, SI unit J kg^-1; for ice L = 336 000 J kg^-1 (80 cal g^-1).
Ice cools better than ice-cold water, snow melts slowly and the surroundings feel colder when snow melts, all because of the large latent heat of fusion of ice.

Questions answered

Define heat and state its SI unit.

Heat is the form of energy that flows from a body at a higher temperature to one at a lower temperature. Its SI unit is the joule (J).

State the relation between the calorie and the joule. How many joules are 50 cal?

1 cal ≈ 4.2 J, so 50 cal = 50 × 4.2 = 210 J.

The temperature of a body rises from 27 °C to 57 °C. Express the rise in kelvin, and express both temperatures in kelvin.

The rise is 30 K, because a degree Celsius and a kelvin are the same size. The temperatures are 300 K and 330 K.

Distinguish between heat capacity and specific heat capacity, and state the SI unit of each.

Heat capacity is the heat needed to raise the temperature of a whole body by 1 K; it depends on mass and material; unit J K^-1. Specific heat capacity is the heat needed to raise the temperature of 1 kg of a substance by 1 K; it depends on the material only; unit J kg^-1 K^-1.

The specific heat capacity of copper is 390 J kg^-1 K^-1. What is the heat capacity of a 2 kg copper block?

C' = m c = 2 × 390 = 780 J K^-1.

How much heat is given out when 0.5 kg of water cools from 90 °C to 40 °C?

Q = m c Δ T = 0.5 × 4200 × 50 = 105 000 J.

State the principle of method of mixtures. On which law is it based?

When a hot body and a cold body are mixed and no heat is lost to the surroundings, the heat lost by the hot body equals the heat gained by the cold body. It is based on the law of conservation of energy.

100 g of water at 70 °C is mixed with 400 g of water at 20 °C. Find the final temperature, neglecting heat losses.

0.1 (70 - T) = 0.4 (T - 20), so 7 - 0.1T = 0.4T - 8, giving 0.5T = 15 and T = 30 ^\circC.

Past board exam questions

ICSE 2027 sample paper · 1 mark

The amount of heat energy required to melt a given mass of a substance at its melting point, without any rise in its temperature is called the:

specific heat capacity
specific latent heat of fusion
latent heat of fusion
heat capacity

Show answer

latent heat of fusion

ICSE 2027 sample paper · 1 mark

A metallic wire is stretched in such a way that its new length becomes twice the original length. How does its specific heat capacity change?

becomes double
becomes 4 times
becomes (1)/(4)
remains the same

Show answer

remains the same

ICSE 2027 sample paper · 2 marks

Blocks of identical material, having masses m, 2m, 3m, 4m, and 5m are heated to 150°C, and then cooled to 50°C. (a) Draw the nature of a graph connecting the amount of heat released vs the mass of the blocks. (b) Write the mathematical expression that enables the determination of the specific heat capacity using the graph.

Show answer

(a) Heat released Q = mcΔt with c and Δt (= 100°C) the same for all blocks, so Q ∝ m: the graph of heat released (y-axis) against mass (x-axis) is a straight line passing through the origin. (b) Specific heat capacity c = slope of the graph/Δt = slope of the graph/100 (Δt = 150°C − 50°C = 100°C).

ICSE 2026 board paper · 1 mark

A metallic wire is stretched in such a way that its new length becomes twice the original length. How does its specific heat capacity change?

becomes double
becomes 4 times
becomes ¼
remains the same

Show answer

remains the same

ICSE 2026 sample paper · 1 mark

Heat capacity of a body is the:

energy needed to melt a body without change in its temperature.
energy needed to raise the temperature of a body by 1°C.
increase in volume of the body when its temperature increases by 1°C.
total amount of internal energy that is constant.

Show answer

energy needed to raise the temperature of a body by 1°C.

ICSE 2026 board paper · 1 mark

Three substances A, B and C of same mass are present at their respective melting points. On heating, if they melt completely in 5 minutes, 7 minutes and 3 minutes respectively, then which substance has the highest specific latent heat? (Assume heat is absorbed at the same rate)

Substance A
Substance B
Substance C
All the substances have same specific latent heat

Show answer

Substance B

ICSE 2026 sample paper · 1 mark

The amount of heat energy required to melt a given mass of a substance at its melting point, without any rise in its temperature is called the:

specific heat capacity.
specific latent heat of fusion.
latent heat of fusion.
specific latent heat of freezing.

Show answer

latent heat of fusion.

ICSE 2026 board paper · 2 marks

A metal piece of thermal capacity 40 JK⁻¹, absorbs 800 J of heat. Calculate the rise in the temperature of this metal piece.

Show answer

Heat absorbed Q = thermal capacity × rise in temperature 800 J = 40 J K⁻¹ × Δt Δt = 800 / 40 = 20 K (i.e. 20 °C).