Question

A steel ball has a diameter of 0.125 m. How much do you need to raise its temperature to make it expand by 0.000200 m (unit=C)?

Answer 1

133 ºC

hope this helps

Answer 2

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]`

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) ]\\`

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) ]`

Replacing all the calculated values in the equation:

`(1.027*10^-3 - 1.022*10^-3)= 34*10^-6*DT\\DT= 0.14[C]`