Question

An aluminium can of cylindrical shape contains 500 cm^3 of water. The area of the inner cross section of the can is 125 cm^2. All measurements refer to 10°c. Find the rise in the water level if the temperature increase to 80°c. The coefficient of linear expansion of aluminium= 23x10^-6/°c and average coefficient of volume expansion of water = 3.2x10^-4/°c.\

Answer 1

# Answer- 0.0765cm

# Solution-

Let the co-efficient of linear expansion of aluminium be a and coefficient of volume expansion of water be y.

The initial area of the bottom A1 and initial volume of water is V1.
The final area is A2.

A2=A1(1+2aT)

because Coefficient of areal expansion = 2a

The final volume of water is V2

V2=V1(1+yT)

The initial length of water is= 500/125=4cm

Final length is= V1(1+yt)/A1(1+2at)

Putting the values we get

Final length=4.0765 cm

Hence

Increase in the water level =(4.0765-4)=.0765 cm