Question

The average coefficient of volume expansion for carbon tetrachloride is 5.81 ? 10-4 (°C)-1. If a 40.5 gal steel container is filled completely with carbon tetrachloride when the temperature is 10.0°C, how much will spill over when the temperature rises to 33.5°C?

Answer 1

Volume of the steel container is V = 40.5 gal

Coefficient of linear expansion of steel is = 12.0 × 10^-6/°C

[ Note: coefficient of linear expansion of steel varies from 11 × 10^-6 /°C to 13 × 10^-6 /°C . So I am taking average value. It does not make much difference with the final answer ]

Average coefficient of volume expansion of carbon tetrachloride is = 5.81 × 10^-4/°C

Initial temperature of the materials under consideration are T1 = 10°C

Final temperature of the container and liquid is T2 = 33.5°C

Change in the temperature of the container and liquid is T = T2- T1 = 23.5°C

Here it is assumed that the container is completely filled with the carbon tetrachloride.

Both the steel container and the liquid expand on heating.

Since the liquid expands more , we can get the volume of liquid spill over by taking the difference between the volumetric expansion of carbon tetrachloride and steel container

Let us calculate the expansion of the steel container

Expansion of steel container V_S = 3 V T

= 3 × 12 × 10^-6 × 40.5 × 23.5

= 0.034 gal

Expansion of the carbon tetrachloride is V_C = V T

= 5.81 × 10^-4 × 40.5 × 23.5

= 0.552 gal

Liquid spill over is V' = V_C - V_S = 0.552 - 0.034 = 0.518 gal

So carbon tetrachloride of volume 0.518 gallon spills over the container.