Question

The coefficient of linear expansion of steel is 11 × 10^-6 per OC. A steel ball has a volume of

exactly 100 cm³ at 0^OC. When heated to 100^OC, what is its volume (in cm³)?

Answer 1

$$\dfrac{\Delta V}{V_0}=\alpha_V \Delta T,$$ $$V_1-V_0=3\alpha_LV_0 \Delta T,$$ $$V_1=V_0(1+3\alpha_L\Delta T),$$ $$V_1=100\ cm^3\cdot(1+3\cdot11\cdot10^{-6}\ ^{\circ}C^{-1}\cdot100\ ^{\circ}C)=100.33\ cm^3.$$