Question

The density of water at 20 degrees celsuis is .9982 g/ml and at 0 degrees celsuis is .9150 g/cm^3.

The volume of a typical soda can is 333ml. Assuming the starting temperature of the can is 20 degrees celsuis and is filled only with water, what volume would the can need to be so that when the water reached 0 degrees celsuis the can would not explode.

Answer 1

It is given that density of water at 20^oC = 0.9982 g/ml and at 0^oC = 0.9150 g/cm³ = 0.9150 g/ml .

But we know that,

Density = Mass / Volume -----------------------------(1)

Here the volume of soda can containing water is given to be 333 ml.

At 20^oC ,

0.9982 g/ml = Mass / 333 ml ----------------------------------From (1)

Mass of water = 0.9982 * 333 = 332.4 g

Thus the mass of water in soda can at 20^oC is 332.4 g .

This mass of water will remain constant even if the temperature of the system decreases.

Hence at 0^oC,

0.9150 g/ml= 332.4 g / Volume ------------------------------From (1)

Volume = 332.4 / 0.9150 = 363.27 ml

Thus the volume of can should be 363.27 ml when water in it reaches at 0^oC to avoid its explosion.