Question

Q2(a) A Pyrex beaker of 400 ml (coefficient of linear expansion = 0.3x10-5 °C) is filled with 350 ml of glycerine (coefficient of volume expansion = 5.1 104c). Analyze if the glycerine will overflow if the temperature of both beaker and glycerine is heated from 25 °C to 100 °C. (5 marks)

please I need solution as soon as possible

Answer 1

2 a. Given, initial volume of beaker, Vib = 400 ml
coeficient of linear expansion ab = 0.3*10^-5

for glycerine, Vig = 350 ml
coefficient of volume expansion, ag = 5.1*10^-4

now, temperature is changed by 75 C
hence,
final volume of beaker is
Vfb = Vib(1 + 3*ab*75) [ we use 3*ab as ab is linear coefficient of expansion, and hence volumetric coefficient of expansion shall be 3*ab]
also, fro glycering,
Vfg = Vig(1 + ag*75)

Vfb = Vib(1 + 3*ab*75)
Vfb = 400(1 + 3*0.3*10^-5*75) = 400.27 ml

and
Vfg = Vig(1 + ag*75)
Vfg = 350(1 + 5.1*10^-4*75) = 363.387 ml
hence, total beaker volume is still greater than volume of expanded glycerine at 100 C after a change of 75 deg
hence the3 glycerine will not overflow