A o (b) Area expansion V T V o V o (c) Volume expansion Figure . Expansion joints for safety - - - - Unit Heat and thermodynamics Solution D L L = α L ΔT ΔL = α L L ∆T ΔL = × − × × = . m= mm Area Expansion For a small change in temperature ΔT the fractional change in area ∆ A of a substance is directly proportional to ΔT and it can be written as D A A = α A ΔT Therefore, α A = D D Where, α A = coefficient of area expansion. ΔA = Change in area A = Original area ΔT = Change in temperature Volume Expansion For a small change in temperature ΔT the fractional change in volume ∆ V of a substance is directly proportional to ΔT.
D V V = α V ΔT Therefore, α V = ∆ ∆ expansion in volume is termed as volume expansion . It is shown in Figure . Linear Expansion In solids, for a small change in temperature ΔT, the fractional change in length ∆ L is directly proportional to ΔT. D L L = α L ΔT Therefore, α L = D D Where, α L = coefficient of linear expansion.
ΔL = Change in length L = Original length ΔT = Change in temperature. • When the lid of a glass bottle is tight, keep the lid near the hot water which makes it easier to open. It is because the lid has higher thermal expansion than glass. • When the hot boiled egg is dropped in cold water, the egg shell can be removed easily.
It is because of the different thermal expansions of the shell and egg. EXAMPLE . Eiffel tower is made up of iron and its height is roughly m. During winter season (January) in France the temperature is °C and in hot