A glass window pane is exactly 23 cm by 38 cm at 10oC. By how much has its area increased when it temperature is 49oC, assuming that it can expand freely? Take the coefficient of thermal expansion for the glass to be exactly 9 x 10-6/Co

Answer 1

Area increases by a factor equal to the square of the length increase factor.

Old area = 23 x 38 = 874 cm^2

New area = (Old area)*(1 + 39*9*10^-6)^2
= 874*(1.000351)^2
= 874.61 cm^2

For small fractional increases such as we have here, the Area increase factor is very nearly twice the Length increase factor.

Anew/Aold = (1 + 2*39*9*10^-6)