Change of density with temperature

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    Change of density with temperature

The density of a substance is defined as its mass per unit volume of a given mass of a substance changes with temperature while its mass remain the same , the density undergoes a change with the temperature .

Consider a body of mass m . Let v₁ and ƍ₁ be its volume and density respectively at temperature t₁ and v₁and ƍ₂ the corresponding values at t₂.

Clearly , mass m= v₂ƍ₂=v₁(1+ƳΔT)ƍ₂, where ΔT=t₂-t₁ ,

Thus ƍ₂ = ƍ₁/(1+ƳΔT) = ƍ₁(1+ƳΔT)^-1. = ƍ₁(1-ƳΔT)[ Using Binomial theorem]

i.e.  ƍ₂= ƍ₁(1-ƳΔT) [so we can say the density of the material decreases with the rise in temperature].

Some numericals  for practice based on change of density with temperature are given below .

1. Coefficient of volume expansion of mercury is 0.18 x 10^-3/⁰C . If the density of mercury at 0⁰C is 13.6g/cc, then its density at 200⁰C is (a) 13.11g/cc (b)52.11g/cc (c)16.11g/cc (d) 26.11g/cc.

2. The coefficient of volume expansion of glycerin is 49×10^-5/K. The fractional change in density on a 30⁰C rise in temperature is (a)1.47 x 10^-2 (b) 1.47 x 10^-3 (c) 1.47 x 10^-1 (d) 1.47 x 10^-4.