Question

The coefficient of volume expansion of glycerin is 49 × 10–5 K–1. What is the fractional change in its density for a 30 °C rise in temperature?

Answer 1

Here,
Coefficient of volume expansion( c) = 49 × 10^-5 /K
Rise in temperature ( ∆T) = 30°C
Let initial volume = Vo
So, volume of Glycerine when temperature is increased by 30°C
V = Vo[ 1 + c∆T]
= Vo[ 1 + 49 × 10^-5×30]
= Vo [ 1 + 147× 10^-4 ]
= Vo( 1 + 0.0147 )
= 1.0147Vo

V = 1.0147Vo
V/Vo = 1.0147

Let mass of glycerine is m then,
Initial density of glycerine (do) = m/Vo
Final density of glycerine ( d) = m/v

So, V/Vo = 1.0147
(m/Vo)/(m/V) = 1.0147
do/d = 1.0147
Now, fraction change in density = ∆d/do
= ( d - do)/do
= d/do - 1
= 1/1.0147 - 1
= -0.0145

Answer 2

Hi!

It is easier to solve this through errors

By error method you can infer that

fractional change in volume =fractional change in density

(∆V/V = ∆d/d)

We know that ∆V/V= coefficient of thermal expansion * change in temperature

Therefore ∆d/d= 4.9*10^-4*30= 1.47*10^-2

Hope I helped!!