-->

Mechanical Properties Of Fluids

Question
CBSEENPH11020035

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?

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

Rise in temperature, Δ= 30°C
Fractional change in its volume = ΔV/V
Relation between fractional change in volume and change in temperature is given by, 
fraction numerator increment straight V over denominator straight V end fraction space equals space straight alpha subscript straight v increment straight T

straight V subscript straight T subscript 2 end subscript space minus space straight V subscript straight T subscript 1 end subscript space equals space space straight V subscript straight T subscript 1 end subscript straight alpha subscript straight V increment straight T space

open parentheses fraction numerator straight m space over denominator straight rho subscript straight T subscript 2 end subscript end fraction close parentheses minus space open parentheses straight m over straight rho subscript straight T subscript 1 end subscript close parentheses equals space open parentheses straight m over straight rho subscript straight T subscript 1 end subscript close parentheses space straight alpha subscript straight V space ΔT space

where comma space
straight m space equals space Mass space of space glycerine

straight rho subscript straight T subscript 1 space end subscript end subscript equals space Initial space density space at space straight T subscript 1
straight rho subscript straight T subscript 2 space end subscript end subscript equals space Initial space density space at space straight T subscript 2

Therefore comma space

fraction numerator straight rho subscript straight T subscript 1 space end subscript end subscript space minus straight rho subscript straight T subscript 2 space end subscript end subscript over denominator straight rho subscript straight T subscript 2 space end subscript end subscript end fraction space equals space Fractional space change space in space density
So comma space

Fractional space change space in space density space of space
glycerine space equals space 49 cross times 10 to the power of negative 5 end exponent cross times 30 space equals space 1.47 space cross times space 10 to the power of – 2 end exponent.