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Fundamentals Of Physics
Found in: Page 541

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Short Answer

Find the change in volume of an aluminum sphere with an initial radius of 10 cm when the sphere is heated from 0.0oC to 100.0oC.

The change in volume of an aluminum sphere is 29 cm3

See the step by step solution

Step by Step Solution

Step 1: The given data

  1. Initial radius of sphere r1=10 cm at T1=0oC
  2. Final temperature at which sphere expands T2=100oC
  3. Linear expansion coefficient for aluminum is α=23×10-6/Co

Step 2: Understanding the concept of linear expansion

When an object's temperature changes, it expands and grows larger, a process known as thermal expansion. Thermal expansion can occur due to an increase in temperature. For the given problem, we have to use the formula for volume expansion. Change in volume expansion depends on the original volume, the temperature change, and the volume expansion coefficient.


The linear expansion of a body, L=T …(i)

Where is the coefficient of linear expansion of body.

The volume change in expansion of a body, V=T …(ii)

Where is the coefficient of volume expansion of the rod

The volume of the sphere, V=43πr3 …(iii)

Step 3: Calculation of the volume change

So, the coefficient of volume expansion of the rod is given as:


Therefore, we can calculate the initial volume of the sphere by using the formula of equation (iii) as given:

V=43×3.14×10 cm3=4186.66 cm3

We can now find the change in volume using equation (ii) as:

V=4186.66 cm3×69×10-6/Co×100-0o C=28.88 cm329 cm3

Hence, the change in volume is 29 cm3

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