A steel bucket is full to the rim with water at 70 degrees Fahrenheit. The bucke

Question

A steel bucket is full to the rim with water at 70 degrees Fahrenheit. The bucket and the water are then cooled to 45 degrees Fahrenheit. Did some water spill out or did all of it stay in the bucket? Coefficient of bulk expansion for steel is 35 x 10 ^-6 1/°C and for water is 210 x 10^-6 1/°C.

A. water level drops in bucket, no spill (the correct answer)
B. water remains full to the rim
C. water spills out of the bucket
D. water boils
E. water freezes in bucket

Can you please explain why the answer is A and how to solve it? My teacher explained it as a matter of ratios, but I don't understand. Thanks

Explanation / Answer

To justify the answer, the following must have taken place:

The volume of the water must have contracted more than that of the volume of the steel bucket. This can be evident from the coefficients of bulk expansion of steel and water given. Since the coefficient of water is more than that of steel bucket, the change in volume of water due to the change in temperature is more than that of steel.

Hence volume of water is more vulnerable to change in temperature than steel. Therefore, the volume of water has contracted more when the temperature is cooled down from 70degrees to 45 degrees than that of the steel bucket.

Since the volume of water is now lesser than that of the bucket, the level of water drops in bucket and no spill takes place.

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