Question

at o°c and 100°c, the length of a metal rod are 1.00 m and 1.02 m respectively, calculate the linear expansivity of the rod​

Answer 1

`\alpha = 0.0002 = 2* 10^-^4 \ \°C^-^1`

Step-by-step explanation:

A rod, as long as it's sufficiently thin, will expand according to the law

`l(t)=l_0(1+\alpha\Delta t)` Where the LHS is the length as a given temperature,
`l_0` is the starting length,
`\alpha` is the linear expansivity coefficient (the one we need) and
`\Delta t` is the difference in temperature. Let's plug values and see what we get:

`1.02m = 1.00m (1+\alpha(100\°C-0\°C))\\1.02=1.00(1+100\alpha) \rightarrow 1.02=1+100\alpha\\0.02=100\alpha \rightarrow \alpha = 0.0002 = 2* 10^-^4 \ \°C^-^1`