**NEET Physics Notes Mechanics-Transfer of heat-Linear Expansion**

**Linear Expansion**

**Linear Expansion**

Thermal expansion along a single dimension of a solid body is defined as the linear expansion.

If a rod is having length l_{0 }at temperature T, then elongation in length of rod due to rise in temperature by ∆T is, \(\Delta l=l_{0} \alpha \Delta T\)

where, a is the coefficient of linear expansion whose value depends on the nature of the material.

If temperature increases, then the rod expands and if temperature decreases, the rod contracts.

**Superficial Expansion or Areal Expansion**

Superficial expansion is also valid only for solids.

where, A0 is the area of the body at temperature T, β is the coefficient of superficial expansion and \(A_{f}\) is the area of the body when temperature has been changed by ∆T

**Volume or Cubical Expansion**

Cubical expansion is seen in all the three states of matter. where symbols have their usual meanings,γ is the coefficient of cubical expansion.

For isotropic solids, γ = 3α. For liquids and gases,γ = 3α is not valid as a is not defined for liquids and gases.

as molecules in gases are more mobile.

As temperature increases, density decreases according to relation,

For isotropic materials, expansion or any other properties are same in all three directions and hence, for isotropic materials,

**Apparent Expansion of Liquid**

If in a beaker (container), a liquid is fully filled and if the temperature of the system increases, then because of the fact that , the expansion in liquid is more than the expansion in solid and thus the liquid overflows from the container. This is termed as apparent expansion of liquid.

Consider a vessel of volume V0 fully filled with a ‘ liquid of coefficient of cubical expansion γ. If temperature of the system is increased by ΔT then

where, subscripts cand 1 denote the container and the liquid respectively.

The volume pf overflowing liquid is

where, is termed as the apparent coefficient of cubical expansion.

**Anomalous/Exceptional Behaviour of Water**

As the temperature of water increases from 0 to 4°C, the density of water increases and as temperature increases beyond 4°C, the density decreases. The variation in the density of water with temperature is shown in the figure given below.

**Specific Heat Capacity**

- When we supply (or withdraw) heat to (or from) a body, two things may occur, its temperature may change or phase may change.
- The quantity of heat Q required to change the temperature of a body of mass m by ΔT, is approximately proportional to the product of m and ΔT, i.e. , where s is the specific heat capacity of the material.
- Specific heat capacity can have any value from 0 to ∝. For some substances under particular situations, it can have negative values also.
- The product of mass of the body and specific heat capacity is termed as heat capacity, C = m x s.
- , i.e. heat capacity is defined as the amount of heat

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

**Molar Heat Capacity**

The amount of heat required to change the temperature of a unit mole of substance by 1°C is termed as its molar heat capacity,

Generally, for gases, two molar heat capacities are very common—molar heat capacity at constant pressure (Cp) and molar heat capacity at constant volume (Cv).