Question

in what way the density of glycerine changes as the temperature increase?

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

Here is your answer...✌✌

Coefficient of volume expansion of glycerin, αV = 49 × 10–5 K–1

Rise in temperature, ΔT = 30°C

Fractional change in its volume = ΔV/V

This change is related with the change in temperature as:

ΔV/V = αV ΔT

VT2 – VT1  =  VT1 αV ΔT

(m /ρT2)- (m /ρT1) = (m /ρT1)αV ΔT

Where,

m = Mass of glycerine

ρT1 = Initial density at T1

ρT2 = Initial density at T2

(ρT1 – ρT2 ) / ρT2  =  Fractional change in density

∴ Fractional change in the density of glycerin = 49 ×10–5 × 30 = 1.47 × 10–2.