Variation in Density with Temperature
In this article we are going to discuss about Variation in Density with temperature of solids and liquids.
We know that on heating a substance, its volume increases but mass remains the same.
Hence we conclude that :-
Heating of bodies is accompanied by an increase in volume and decrease in density.
M = mass of a substance
V0 = initial volume, ρ0 = initial density
ΔT = change in temperature
γ = coefficient of volume expansion of the substance
V = final volume, ρ = final density
Since mass remains the same ⇒ M = V0ρ0 = Vρ
Now final volume is given by V = V0(1 + γΔT)
Dividing both sides by M, we get
Now as γΔT<<<1, hence
This is the expression to find final density of a material after an increase in temperature of ΔT.
Example. A sphere of diameter 7 cm and mass 266.5 gm floats in a bath of a liquid. As the temperature rises, the sphere begins to sink & at a temperature of 35ºC the sphere gets completely submerged. If the density of a liquid at is 1.527 gm/cc, then neglecting the expansion of the sphere, find the coefficient of cubical(volume) expansion of the liquid.
Solution. Volume of the sphere =
∴ Density of sphere = 266.5/179.59 = 1.484 g/cc
The density of the material of the sphere and the density of the liquid becomes equal at the moment when the sphere is just submerged in the liquid.
γ = 8.27×10-4 ºC-1