# Physics > Thermal Properties of matter

• Heat is the form of energy transferred between two (or more) systems or a system and its surroundings by virtue of temperature difference. The SI unit of heat energy transferred is expressed in joule (J) while SI unit of temperature is kelvin  and °C is a commonly used unit of temperature.
• A relationship for converting between the two scales may be obtained from a graph of Fahrenheit temperature versus Celsius temperature  in a straight line , whose equation is

Ideal gas equation:

where, μ is the number of moles in the sample of gas and R is called universal gas constant:

• The absolute minimum temperature for an ideal gas, is found to be  °C and is designated as absolute zero.
• The size of the unit for Kelvin temperature is the same celsius degree, so temperature on these scales are related by

• A change in the temperature of a body causes change in its dimensions. The increase in the dimensions of a body due to the increase in its temperature is called thermal expansion. The expansion in length is called linear expansion. The expansion in area is called area expansion. The expansion in volume is called volume expansion.
• If the substance is in the form of a long rod, then for small change in temperature, , the fractional change in length, , is directly proportional to
• where  is known as the coefficient of linear expansion.

• The fractional change in volume, , of a substance for temperature change  and define the coefficient of volume expansion,  as

for ideal gas.

• The change in temperature of a substance, when a given quantity of heat is absorbed or rejected by it, is characterised by a quantity called the heat capacity of that substance. We define heat capacity, S of a substance as

where  is the amount of heat supplied to the substance to change its temperature from  to

• Every substance has a unique value for the amount of heat absorbed or rejected to change the temperature of unit mass of it by one unit. This quantity is referred to as the specific heat capacity of the substance.

The specific heat capacity is the property of the substance which determines the change in the temperature of the substance when a given quantity of heat is absorbed (or rejected) by it. It is defined as the amount of heat per unit mass absorbed or rejected by the substance to change its temperature by one unit. It depends on the nature of the substance and its temperature.

The SI unit of specific heat capacity is

If the amount of substance is specified in terms of moles , instead of mass  in kg, we can define heat capacity per mole of the substance by

where C is known as molar specific heat capacity of the substance.

• A device in which heat measurement can be made is called a calorimeter.
• The change of state from solid to liquid is called melting and from liquid to solid is called fusion. It is observed that the temperature remains constant until the entire amount of the solid substance melts. That is, both the solid and liquid states of the substance coexist in thermal equilibrium during the change of states from solid to liquid. The temperature at which the solid and the liquid states of the substance in thermal equilibrium with each other is called its melting point. It is characteristic of the substance. It also depends on pressure. The melting point of a substance at standard atmospheric pressure is called its normal melting point.
• The change of state from liquid to vapour (or gas) is called vaporisation.
• The temperature at which the liquid and the vapour states of the substance coexist is called its boiling point.
• The change from solid state to vapour state without passing through the liquid state is called sublimation, and the substance is said to sublime. Dry ice (solid CO2) sublimes, so also iodine. During the sublimation process both the

solid and vapour states of a substance coexist in thermal equilibrium.

• if mass m of a substance undergoes a change from one state to the other, then the quantity of heat required is given by

or

where  is known as latent heat and is a characteristic of the substance. Its SI unit is . The value of L also depends on the pressure.

• Conduction is the mechanism of transfer of heat between two adjacent parts of a body because of their temperature difference.
• the rate of flow of heat (or heat current) H is proportional to the temperature difference  and the area of cross section  and is inversely proportional to the length  :
• The constant of proportionality  is called the thermal conductivity of the material.

• Convection is a mode of heat transfer by actual motion of matter. It is possible only in fluids. Convection can be natural or forced. In natural convection, gravity plays an important part. When a fluid is heated from below, the hot part expands and, therefore, becomes less dense. Because of buoyancy, it rises and the upper colder part replaces it. This again gets heated, rises up and is replaced by the colder part of the fluid. The process goes on. This mode of heat transfer is evidently different from conduction. Convection involves bulk transport of different parts of the fluid.
• Newton's Law of Cooling says that the rate of cooling of a body is proportional to the excess temperature of the body over the surroundings :

Where  is the temperature of the surrounding medium and  is the temperature of the body.

### Sample Examples

#### Question

A blacksmith fixes iron ring on the rim of the wooden wheel of a bullock cart. The diameter of the rim and the iron

ring are  and  respectively at 27 °C. To what temperature should the ring be heated so as to fit the rim of the wheel?

Given,  °C

or

#### Question

A sphere of aluminium of  placed for sufficient time in a vessel containing boiling water, so that the sphere is at . It is then immediately transferred to  copper calorimeter containing  of water at . The temperature of water rises and attains a steady state at . Calculate the specific heat capacity of aluminium.

#### Solution

Mass of aluminium sphere

Initial temp. of aluminium sphere =

Final temp. =

Change in temp

Let specific heat capacity of aluminium be

The amount of heat lost by the aluminium sphere

Mass of water

Mass of calorimeter

Initial temp. of water and calorimeter =

Final temp. of the mixture =

Change in temp. (ΔT2) =

Specific heat capacity of water

Specific heat capacity of copper calorimeter

The amount of heat gained by water and calorimeter

=

=

In the steady state heat lost by the aluminium sphere = heat gained by water + heat gained by calorimeter.

So,