The volume of a metal sphere is increased by `2%` of its original volume when it is heated from `300 K` to `604 K`. Calculate the coefficient of linear, superficial and cubical expansion of the metal.

Answer

`[2.19xx10^(-5) .^(@)C^(-1); 4.38xx10^(-5) .^(@)C^(-1); 6.58xx10^(-5) .^(@)C^(-1)]`

Explanation

Here, `(Delta V)/(V)=(2)/(100)` or `DeltaV=(2V)/(100)=(V)/(50)`
`DeltaT=604-300=304 K`
`Delta T=V gamma Delta T` or `(V)/(50)=Vxxgammaxx304`
or `gamma=(1)/(50xx304)=6.58xx10^(-5) .^(@)C^(-1)`
`alpha=(gamma)/(3)=(6.58)/(3)xx10^(-5)=2.19xx10^(-5) .^(@)C^(-1)`
`alpha=2 alpha=2xx2.19xx10^(-5)=4.38xx10^(-5) .^(@)C^(-1)`