Problem 2: A copper sphere of radius 5cm is heated from 0^oC to 200^oC. What will be the change in volume?

Solution:

Step:1 Overview

It is a matter of daily observation that in general bodies undergo change in size when they are heated. This change in size when heating is termed as Thermal Expansion. Thermal expansion can be divided into two types:

1. Linear Expansion
2. Volume Expansion

Volume expansion of solid bodies depends upon a constant known as Beta, which has different values for different bodies. Value of Beta for copper is:

β=51x10^-6K^-1

And the equation of volume expansion is given by:

ΔV=βVΔT

Volume of sphere with given radius can be found by given formula:

V=4.19r³

Step:2 Calculation

Initial Volume of sphere:

V=4.19(0.05m)³
V=5.24x10^-4m³

Change in temperature:

ΔT=T₂-T₁ΔT=437K-237K=200K

Change in volume:

ΔV=(51x10^-6K^-1)(5.24x10^-4m³)(200K)
ΔV=5.34x10^-6m³(Ans)