An aluminum cup of 150 cm3 capacity is completely filled with glycerin at 23°C. How much glycerin will spill out of the cup if the temperature of both the cup and glycerin is increased to 41°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°.

1.19cm^3 of glycerine

Explanation:

Let Vo = 150cm^3 for both aluminum and glycerine, using expansion formula:

Volume of spill glycerine = change in volume of glycerine - change in volume of aluminum

Volume of glycerine = coefficient of volume expansion of glycerine * Vo * change in temperature - coefficient of volume expansion of Aluminum*Vo * change temperature

coefficient of volume expansion of aluminum = coefficient of linear expansion of aluminum*3 = 23*10^-6 * 3 = 0.69*10^-4 oC^-1

Change in temperature = 41-23 = 18oC

Volume of glycerine that spill = (5.1*10^-4) - (0.69*10^-4) (150*18) = 4.41*10^-4*2700 = 1.19cm3