Question

A copper cylinder is I initially at 20.0°C. At what temperature will it's volume be 0.150% larger than it is at 20.0°C

Answer 1

The change of volume during the termal expansion is given as follows:

$$\dfrac{\Delta V}{V} = \alpha (T_f -T_i)$$

where $\Delta V/V = 0.15\% = 0.0015$ is the relative volume change, $\alpha = 51\times 10^{-6}\space \degree C^{-1}$ is the volumetric thermal expansion coefficient of copper, $T_i = 20.0\degree C$ is the initial temperature, and $T_f$ is the unknown final temperature. Expressing $T_f$, find:

$$T_f = T_i + \dfrac{1}{\alpha}\dfrac{\Delta V}{V}\\ T_f = 20\degree C + \dfrac{1}{51\times 10^{-6}\space \degree C^{-1}}\cdot 0.0015 \approx 49\degree C$$

Answer. $49\degree C$.