Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

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. - Physics

Answer in Brief

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 is 23 × 10–6 °C–1 and the average coefficient of the volume expansion of water is 3.2 × 10–4 °C–1.

Advertisement Remove all ads

Solution

Given:
Volume of water contained in the aluminium can, V0 = 500 cm3
Area of inner cross-section of the can, A = 125 cm2
Coefficient of volume expansion of water, γ​ = 3.2 × 10–4 °C–1 
Coefficient of linear expansion of aluminium, 

\[\alpha_{AL}\] = 23 × 10–6 °C–1
If  \[∆ \theta\]  is the change in temperature, then final volume of water

\[\left( V \right)\] due to expansion,
V = V0(1 + γΔθ)
   = 500 [1 + 3.2 × 10–4 × (80 – 10)]
   = 500 [1 + 3.2 × 10–4 × 70]
   = 511.2 cm3
The aluminium vessel expands in its length only.
So, area of expansion of the base can be neglected.
Increase in volume of water = 11.2 cm3 
Consider a cylinder of volume 11.2 cm3
∴ Increase in height of the water

\[= \frac{11 . 2}{125}\] = 0.0896

  = 0.089 cm

Concept: Measurement of Temperature
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 1 Heat and Temperature
Q 23 | Page 13
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×