Heat capacity of any body is equal to the amount of heat energy required to increase its temperature through 1°C.

Heat capacity = me

where c = specific heat of the substance of the body and m = mass of the body.

Its SI unit is joule/kelvin (J/K).

• Water Equivalent

It is the quantity of water whose thermal capacity is same as the heat capacity of the body. It is denoted by W.

W = ms = heat capacity of the body.

• Latent Heat

The heat energy absorbed or released at constant temperature per unit mass for change of state is called latent heat.

Heat energy absorbed or released during change of state is given by

Q = mL

where m = mass of the substance and L = latent heat.

Its unit is cal/g or J/kg and its dimension is [L²T^-2].

For water at its normal boiling point or condensation temperature (100°C), the latent heat of vaporisation is

L = 540 cal/g

= 40.8 kJ/ mol

= 2260 kJ/kg

For water at its normal freezing temperature or melting point (0°C), the latent heat of fusion is

L = 80 cal/ g = 60 kJ/mol

= 336 kJ/kg

It is more painful to get burnt by steam rather than by boiling was 100°C gets converted to water at 100°C, then it gives out 536 heat. So, it is clear that steam at 100°C has more heat than wat 100°C (i.e., boiling of water).

After snow falls, the temperature of the atmosphere becomes very This is because the snow absorbs the heat from the atmosphere to down. So, in the mountains, when snow falls, one does not feel too but when ice melts, he feels too cold.

There is more shivering effect of ice cream on teeth as compare that of water (obtained from ice). This is because when ice cream down, it absorbs large amount of heat from teeth.

• Melting

Conversion of solid into liquid state at constant temperature is melting.

• Evaporation

Conversion of liquid into vapour at all temperatures (even below boiling point) is called evaporation.

• Boiling

When a liquid is heated gradually, at a particular temperature saturated vapour pressure of the liquid becomes equal to atmospheric pressure, now bubbles of vapour rise to the surface d liquid. This process is called boiling of the liquid.

The temperature at which a liquid boils, is called boiling point The boiling point of water increases with increase in pre sure decreases with decrease in pressure.

• Sublimation

The conversion of a solid into vapour state is called sublimation.

• Hoar Frost

The conversion of vapours into solid state is called hoar fr..

• Calorimetry

This is the branch of heat transfer that deals with the measorette heat. The heat is usually measured in calories or kilo calories.

Principle of Calorimetry

When a hot body is mixed with a cold body, then heat lost by ha is equal to the heat gained by cold body.

Heat lost = Heat gain

• Thermal Expansion

Increase in size on heating is called thermal expansion. There are three types of thermal expansion.

1. Expansion of solids
2. Expansion of liquids
3. Expansion of gases

1. Expansion of Solids

Three types of expansion -takes place in solid.

Linear Expansion Expansion in length on heating is called linear expansion.

Increase in length

l₂ = l₁(1 + α Δt)

where, l_l and l₂ are initial and final lengths,Δt = change in temperature and α = coefficient of linear expansion.

Coefficient of linear expansion

α = (Δl/l * Δt)

where 1= real length and Δl = change in length and

Δt= change in temperature.

Superficial Expansion Expansion in area on heating is called superficial expansion.

Increase in area A₂ = A₁(1 + β Δt)

where, A₁ and A₂ are initial and final areas and β is a coefficient of superficial expansion.

Coefficient of superficial expansion

β = (ΔA/A * Δt)

where. A = area, AA = change in area and At = change in temperature.

Cubical Expansion Expansion in volume on heating is called cubical expansion.

Increase in volume V₂ = V₁(1 + γΔt)

where V₁ and V₂ are initial and final volumes and γ is a coefficient of cubical expansion.

Coefficient of cubical expansion

Where V = real volume, AV =change in volume and Δt = change in temperature.

Relation between coefficients of linear, superficial and cubical expansions

β = 2α and γ = 3α

Or α:β:γ = 1:2:3

2. Expansion of Liquids

In liquids only expansion in volume takes place on heating.

(i) Apparent Expansion of Liquids When expansion of th container containing liquid, on heating is not taken into accoun then observed expansion is called apparent expansion of liquids.

Coefficient of apparent expansion of a liquid

(ii) Real Expansion of Liquids When expansion of the container, containing liquid, on heating

is also taken into account, then observed expansion is called real expansion of liquids.

Coefficient of real expansion of a liquid

Both, y_r, and y_a are measured in °C^-1.

We can show that y_r = y_a + y_g

where, y_r, and y_a are coefficient of real and apparent expansion of liquids and y_g is coefficient of cubical expansion of the container.

Anamalous Expansion of Water

When temperature of water is increased from 0°C, then its vol decreases upto 4°C, becomes minimum at 4°C and then increases. behaviour of water around 4°C is called, anomalous Expansion water.

3. Expansion of Gases

There are two types of coefficient of expansion in gases

1. Volume Coefficient (& gamma; v) At constant pressure, the change in volume per unit volume per degree celsius is called volume coefficient.

where V₀, V₁, and V₂ are volumes of the gas at 0°C, t₁°C and t₂°C.

2. Pressure Coefficient (γ_p) At constant volume, the change in pressure per unit pressure per degree celsius is called pressure coefficient.

Where p₀, p₁ and p₂ are pressure of the gas at 0°C, t₁° C and t₂° C.