Question

An aluminum cup of 52 cm3 capacity is completely filled with glycerin at 24°C. How much glycerin will spill out of the cup if the temperature of both the cup and glycerin is increased to 33°C? (The linear expansion coefficient of aluminum is 23 × 10-6 1/C°. The coefficient of volume expansion of glycerin is 5.1 × 10-4 1/C°.)

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Answer 1

given

V = 52 cm^3
T1 = 24 C
T2 = 33 C
The linear expansion coefficient of aluminum, alfa_aluminum = 23*10^-6 1/C
The coefficient of volume expansion of glycerin, gamma_glycerin = 5.1*10^-4 1/C

from the given value, The coefficient of volume expansion of alunimum, gamma_alunimum = 3*alfa_alunimum

= 3*23*10^-6

= 69*10^-6 1/C

change in volume of glycerin, delta_V_gycerin = V*gamma_glycerin*(T2 - T1)

= 52*5.1*10^-4*(33 - 24)

= 0.23868 cm^3

change in volume of aluminum, delta_V_alunimum = V*gamma_alunimum*(T2 - T1)

= 52*69*10^-6*(33 - 24)

= 0.032292 cm^3

the volume of glycerin spill out = delta_V_gycerin - delta_V_alunimum

= 0.23868 - 0.032292

= 0.206388 cm^3 <<<<<<<<<--------------Answer