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

Answer:

The temperature raise is = 0.14 [C]

Explanation:

In order to find the temperature difference we must use the following equation:

$V=V_{0} *\beta *DT\\where:\\V = final volume [m^{3} ]\\V_{0} = original volume [m^{3} ]\\\beta =34*10^-6[\frac{1}{C} ]\\DT= temperature difference [C]$

But first we need to find the original volume V:

$V0 = \frac{4}{3} *\pi *r^{3} \\D = diameter = 0.125 [m]\\r = radius =0.0625[m]\\replacing\\V=\frac{4}{3} *\pi *(0.0625^{3} )\\V0=1.022[m^{3} ]$

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:

$V=\frac{4}{3} *\pi *(0.0626)^{3} \\V=1.027*10^-3[m^{3} ]$

Replacing all the calculated values in the equation:

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