PROBLEM (a) Estimate the fractional change in the volume of Earth's oceans due to an average temperature change of 1C. (b) Use the fact that the average depth of the ocean is 4.00 x 103 m to estimate the change in depth. Note that water = 2.07 x 10'4(C)'1. STRATEGY In part (a) solve the volume expansion expression for AV/V. For part (b) use linear expansion to estimate the increase in depth. Neglect the expansion of landmasses, which would reduce the rise in sea level only slightly. SOLUTION (A) Find the fractional change in volume. Divide the volume expansion equation AV = VOAT by V0 and substitute. AV _4 _1 _4 To = BAT: (2.07 x 10 (C) )(1C) = 2 x 10 (B) Find the approximate increase in depth. Use the linear expansion equation. L AT _ [3' L AT Divide the volume expansion AL = 0c 0 _ E 0 coefficient of water by 3 to get the AL (6.90 x 10'5(C)_1)(4,000 m)(1C) z 0.3 m equivalent linear expansion coefficient. LEARN MORE REMARKS Three-tenths of a meter may not seem significant, but combined with increased melting of land-based polar ice caps, some coastal areas could experience flooding. An increase of several degrees increases the value of AL several times and could significantly reduce the value of waterfront property. QUESTION Assuming all have the same initial volume, compare the following substances by the amount of volume expansion due to an increase in temperature: glass, mercury, aluminum, ethyl alcohol. (See this table.) 0 glass > mercury > aluminum > ethyl alcohol 0 mercury > ethyl alcohol > glass > aluminum 0 mercury > ethyl alcohol > aluminum > glass 0 ethyl alcohol > glass > mercury > aluminum 0 glass > ethyl alcohol > aluminum > mercury PRACTICE IT Use the worked example above to help you solve this problem. (a) Estimate the fractional change in the volume of Earth's oceans due to an average temperature change of 3C. Note that [3 = 2.07 x 10_4(C)'1. AV 7:: water (b) Use the fact that the average depth of the ocean is 4.00 x 103 m to estimate the change in EXERCISE HINTS: GETTINGSTARTED | I'M STUCK! A 3.00-liter aluminum cylinder at 500C is filled to the brim with gasoline at the same temperature. If the aluminum and gasoline are warmed to 58.0C, how much gasoline spills out? Hint: Be sure to account for the expansion of the container. Also, ignore the possibility of evaporation, and assume the volume coefficients are good to three digits. (The coefficient of linear expansion for aluminum and the coefficient of volume expansion for gasoline are given in this table.)