OpenStax College Physics for AP® Courses, Chapter 13, Problem 14 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. The rise in sea level due to global warming will, in part B, due to an increased amount of water in the ocean due to ice caps melting. But in addition to that, there is going to be a rise in sea level due to thermal expansion of the water itself. And it's that component of the sea level rise that we are going to be interested in this question. So we consider a column of water that's one kilometer high which is one times 10 to the three meters. And we suppose that change in temperature of the water of one Celsius degree. So by how much will this column of water go up? Now, we know that the coefficient of volume expansion is approximately three times coefficient of linear expansion. And we need to know that because we are going to suppose that water has this coefficient of linear expansion which of course you won’t find in this table because it's a liquid. But we are going to imagine that it does have a coefficient of linear expansion and that's going to be one third of its coefficient of volume expansion. So change in length of this column of water will be this extrapolated or calculated coefficient of linear expansion which is one third the volume coefficient times the original length times the change in temperature. So we have 210 times 10 to the minus six per Celsius degree, which is what it shows here, and divide that by three, multiply by one times 10 to the three meters times one Celsius degree, and that is 7.00 centimeters.