Question

An aluminum cup of 168 cm³ capacity is completely filled with glycerin at 22 °C. How much glycerin, if any, will spill out of the cup if the temperature of both the cup and the glycerin is increased to 34 °C? Give your answer in cm³, but enter only the numerical part in the box.

For reference, glycerin's coefficient of volume expansion = 5.1 x 10^-4/C°. Aluminum's coefficient of linear expansion = 2.3 x 10^-5/C°.

Answer 1

given
V_aluminum = V_glycerin = 168 cm^3

glycerin's coefficient of volume expansion, gamma_glycerin = 5.1*10^-4 /C
Aluminum's coefficient of linear expansion, alfa = 2.3*10^-5 /C
Aluminum's coefficient of volume expansion, gamma_aluminum = 3*alfa

= 3*2.3*10^-5

= 6.9*10^-5 /C

increase in volume of glycerin, delta_V_glycerin = V_glycerin*gamma_glycerin*(Tf - Ti)

= 168*5.1*10^-4*(34 - 22)

= 1.028 cm^3

increase in volume of cup, delta_V_cup = V_aluminum*gamma_aluminum*(Tf - Ti)

= 168*2.3*10^-5*(34 - 22)

= 0.0464 cm^3

the volume of glycerin spill out from the cub = delta_V_glycerin - delta_C_cup

= 1.028 - 0.0464

= 0.982 cm^3 <<<<<<<-------------------Answer