An aluminum sphere is 8.75 cm in diameter. What will be its % change in volume if it is heated from $30 ^\circ \textrm{C}$ to $160 ^\circ \textrm{C}$?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Percent change in volume of the sphere is going to be its final volume minus its initial volume divided by the initial volume times 100%. So, the final volume will be the initial volume plus the heat change in volume. And we can see that the vi's will make 0 here. And we're left with Δv over vi times 90%. Now, the change in volume is the coefficient of volume expansion times the initial volume times the change in temperature. So, we'll substitute that in place of Δv here. And we can see the vi’s cancel here. So, the percent change in volume is the coefficient of volume expansion times the change in temperature times 100%. So, for aluminium a coefficient of volume expansion is 75 times 10 to the minus 6. And multiply that by the final temperature of 160 degrees Celsius minus the initial temperature of 30 degrees Celsius times by 100%. And you get 0.98% will be the change in volume.