Answer:
The temperature raise is = 0.14 [C]
Step-by-step explanation:
In order to find the temperature difference we must use the following equation:
![V=V_(0) *\beta *DT\\where:\\V = final volume [m^(3) ]\\V_(0) = original volume [m^(3) ]\\\beta =34*10^-6[(1)/(C) ]\\DT= temperature difference [C]](https://img.qammunity.org/2020/formulas/physics/high-school/qfaxralh41n13vf30qqffwmy6ix7iwl91p.png)
But first we need to find the original volume V:
![V0 = (4)/(3) *\pi *r^(3) \\D = diameter = 0.125 [m]\\r = radius =0.0625[m]\\replacing\\V=(4)/(3) *\pi *(0.0625^(3) )\\V0=1.022[m^(3) ]\\](https://img.qammunity.org/2020/formulas/physics/high-school/huo063zsrn3dfqegn6qvi05cjaftxrfab6.png)
When the volume is increased the diameter will be larger:
D1 = 0.125[m] + 0.0002[m] = 0.1252[m]
Therefore the new radius will be:
r1=0.0626[m]
The new volume is:
![V=(4)/(3) *\pi *(0.0626)^(3) \\V=1.027*10^-3[m^(3) ]](https://img.qammunity.org/2020/formulas/physics/high-school/c32yvayahkzpwo6n1vsuddltemwlo58573.png)
Replacing all the calculated values in the equation:
![(1.027*10^-3 - 1.022*10^-3)= 34*10^-6*DT\\DT= 0.14[C]](https://img.qammunity.org/2020/formulas/physics/high-school/3lxut9wpbgs4f5ezez7g0rf1msp3kijhvl.png)