Question

An aluminium can of cylindrical shape contains 500 cm³ of water. The area of the inner cross-section of the can is 125 cm². All measurements refer to 10°C. Find the rise in the water level if the temperature increases to 80°C. The coefficient of linear expansion of aluminium = 23 x 10^-6/°C and the average coefficient of volume expansion of water = 3.2 x 10^-4/°C respectively.

Answer 1

Volume of water = 500cm³
Area of cross section of can = 125m²
Final Volume of water
= 500(1 + γΔθ ) = 500[1 + 3.2 × 10^–4 × (80 – 10)] = 511.2 cm³
The aluminium vessel expands in its length only so area expansion of base cab be neglected.
Increase in volume of water = 11.2 cm³
Considering a cylinder of volume = 11.2 cm³
Height of water increased =11.2/125 = 0.089 cm