A sheet of metal has a hole of diameter 10cm. If the sheet is heated by 100c what will be the diameter of the hole?
Question
A sheet of metal has a hole of diameter 10cm. If the sheet is heated by 100c what will be the diameter of the hole?
Solution
To answer this question, we need to know the coefficient of linear expansion of the metal. The coefficient of linear expansion (α) is a material-specific constant that measures the degree to which a material expands for each degree increase in temperature.
The formula to calculate the change in length (or in this case, diameter) due to thermal expansion is:
ΔL = α * L0 * ΔT
where:
- ΔL is the change in length (or diameter),
- α is the coefficient of linear expansion,
- L0 is the initial length (or diameter), and
- ΔT is the change in temperature.
However, without the coefficient of linear expansion, we cannot calculate the exact change in diameter of the hole.
It's also important to note that if the sheet of metal expands when heated, the hole in it will also expand, contrary to what might be some people's first guess.
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