Question

Question #e675f

Answer 1

Linear expansion coefficients have units of K^(-1) and typical values around `1times10^(-5) K^(-1)`, so we rewrite the question as: If an object initially at 29C with a length of 5.00 m and expansion coefficient of `1times10^(-5) K^(-1)` is heated to 29C, what is the new length of the expanded object?

Explanation:

The strain that occurs during expansion (fractional change in length) is
`epsilon=(dL)/L=alpha(T_2-T_1)=1times10^(-5)(29-28)=1times10^(-5)`

The expansion is
`dL=Ltimesalpha=5mtimes1times10^(-5)=5times10^(-5)m`

The new length is
`L + dL= 5m+1times10^(-5)m=5.00005m`