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 increases to 80°C. The coefficient of linear expansion of aluminium = 23 × 10 –6 °C –1 and the average coefficient of volume expansion of water = 3.2 × 10 –4 °C –1 respectively.

Question

Philoid · Accepted Answer

Given:

Volume of water in Aluminium Can : V_w = 500 cm³.

Area of the inner cross section of the can : A = 125 cm².

Initial Temperature while measuring: T₁ = 10 ° C.

Increased temperature : T₂ = 80 °C

Thus, Change in Temperature : Δ T = T₂-T₁ = 80-10= 70 ° C.

The coefficient of linear expansion of aluminium :α=23×10^–6 °C^–1.

The Average coefficient of volume expansion of water:
γ=3.2×10^–4 °C^–1.

We need to find the increased height of the water level when temperature is increased to 80° C.

First Let’s calculate the increased volume of water.
Formula Used:

The formula for Volume Expansion of a body is:

Here V’ is the changed volume of the body( in this case water) at T₂ due to expansion and V is the initial volume at T₁

Substituting the given values ,we get:

Thus the final volume of water after temperature increase is 511.2 cm³.

Now, The aluminium can will be expanded too due to temperature increase.

But it’s linear expansion is along it’s length only. Which means that area expansion can be neglected.

Since we got the Final Volume and Initial volume of Water and neglecting area expansion we can find out the height of the increased water level.

Now,

Rise in water level is given by :

Hence the rise in the water level if the temperature increases to 80°C is 0.0896 cm.