(i) Linear Expansion: Consider a rod of length l₁ at a temperature T₁. Let it be an overheated to a temperature T₂ and the increased length of the rod is l₂ then 

            l₂= l₁ (1+ αΔt)

            a = Coefficient of linear relation and Δt=T₂-T₁

(ii) Superficial Expansion (expansion in surface area): If A₁ is the area of solid at T₁ °C and A₂ is the area at T₂°C . Then   A₂ = A₁(1 + Δt )     

 Coefficient of superficial (areal) expansion and Δt=T₂-T₁

(iii) Volume expansion (Part A: expansion in solids): If V₁ is the volume of solid at T₁°C and V₂ is the volume at T₂ °C then,           V₂ = V₁(1+γΔt)

 Coefficient of volume relation and Δt=T₂-T₁

If d₁ is the density at T₁°C, d₂ is the density at T₂°C th

            d₂ = d₁/(1+yDt) or d₂ = d₁/(1-yDt) where Dt=T₂-T₁

(iv) Expansion of gases:

Pressure coefficient of a gas is the ratio of increase in pressure for 1°C rise in temperature to the pressure at 0°C, provided the volume of the gas is kept constant.      γ_p =(p_t-p_o)/p_ot

Where             γ_p = pressure coefficient

                        P_t­ = pressure at t°C    

                        P_o= pressure at 0°C

Volume coefficient of a gas is similarly defined as (pressure being kept constant),  g_v =(v_t-v_o)/v_ot

Where             γ_v = volume coefficient          

                        V_t = volume at t°C

                        V_o= volume at 0°C

Experiments have shown the value of  γ_p (or γ_v) is the same for all gases and equal to 1/273 per degree Celsius, i.e.            γ_p = γ_v =  per°C or 1/273 per K,

Where K denotes for absolute of Kelvin temperature

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