# Measurement of Heat in Physics

Measurement of Heat:

Heat is a form of energy. Amount of thermal energy absorbed or given out by a body cannot be measured directly by any instrument. Quantities of heat must be measured by the effect they produce.

Unit of heat:

Since heat is a form of energy, it is measured in Joule, in the same way as other forms of enrgy.
Historically water was the standard substance for defining heat units. This unit in CGS is called calorie.

Calorie:

It is defined as the quantity of heat required to raise the temperature of one gram of water through 1°C from 14.5°C to 15.5°C.
1 Calorie = 4.2 joule

Heat capacity of a body

It is the quantity of heat required to raise the temperature of the body by one Kelvin
Unit: joule/kelvin = JK-1

Specific heat capacity of a substance (c)

It is the quantity of heat required to raise the temperature of unit mass of the substance through one Kelvin.
Unit: joule per kg per Kelvin (J kg-1 K-1)
Dimensions: L2T-2K-1

Specific heat capacity of some substance in different unit

 Substance J kg-1 K-1 kJ kg-1 K-1 Jg-1K-1 Water 4200 4.2 Copper 378 0.378 0.378 Aluminium 924 0.924 0.924

Water equivalent:

Water equivalent of a body is the mass of water having the same heat capacity as the given body.
In SI Unit, water equivalent (in kg) = Heat capacity of body/ Sp. Heat capacity of water.

Relation between quantity of heat and rise of temperature:

Let m be the mass of the body and c its specific heat. When a quantity of heat Q is supplied, let the temperature rise by θ°C, then,

Q = mcθ

Principle of mixtures:

When a hot body is allowed to share its heat with a cold body, there is a flow of heat from the hot body to the cold body until both attain a common temperature. Then if no heat is lost to or gained from the surrounding,

Heat lost by the hot body = Heat gained by the cold body.

Change of state (change of phase)

A substance may exists in one of the three states, solid, liquid or gas, depending on the temperature. A change of state can be affected by the addition or subtraction of heat from a substance. The change from solid to liquid is known as fusion (melting) and the reverse change from liquid to solid is known as freezing (solidification). The change from liquid to vapour is known as vapourization and the reverse change is known as condensation.

Laws of fusion

1. Every crystalline substance, when heated, melts at a particular temperature called melting point of the substance.
2. During melting, the temperature remains steady until the whole substance has melted.
3. Unit mass of substance at its melting point requires a definite quantity of heat to change it from solid to the liquid state without change of temperature. This quantity of heat is called specific latent heat of fusion of the substance (simply latent heat).
4. The volume of a solid change during melting. Some substance like ice contracts on melting, while others like wax expands on melting.
5. A change of pressure changes the melting point. For substance like ice, an increase of pressure, lowers the melting point, whereas for substances like wax an increase of pressure raises the melting point.

Specific latent heat of fusion of a solid (L)

It is the quantity of heat required to convert unit mass of the solid at its melting point into liquid at the same temperature.

Unit: J/kg

Quantity heat required to convert a solid of mass m and specific latent heat L into liquid without any change of temperature is,

Q = mL

Specific latent heat of fusion of ice is the quantity of heat required to convert unit mass of ice at 0°C (273 K) to water at the same temperature.

Sp. latent heat of fusion of ice, L = 336000 = 3.36 x 105 J/kg

Boiling (Ebullution)

Laws of boiling

1. Every liquid boils at a particular temperature called boiling point of the liquid.

2. During boiling temperature remains steady until the whole liquid has vaporised.

3. Unit mass of liquid at its boiling point requires a definite quantity of heat for its conversion into vapour state. This is known as latent heat of vapourisation.

4. An increase of pressure raises the boiling point of the liquid.

Specific latent heat of vapourisation of a liquid (L)

It is the quantity of heat required to convert unit mass of liquid at its boiling point into vapour at the same temperature.

Unit: J/kg

Quantity of heat required to convert a liquid of mass m and specific latent heat L into vapour without any change of temperature, Q = mL

Specific latent heat of steam is the quantity of heat required to convert unit mass of water at 100°C (373 K) to steam at the same temperature. ,

Latent heat of steam = 2268000 J/kg. = 2.268 x 106 J/kg