Posted by marie on Monday, January 24, 2011 at 7:27pm.
137 x 10^7 km^3
1.03 g / cm^3
4.184 g / cm^3
We need to convert the volume of the oceans to cm^3 so density (g/cm^3 is in the same units.
1 km = 1000 meters
1 meter = 39.37 inches
1 inch = 2.54 cm
1 km x (1000 meters / 1km) = 1000 meters
1000 meters x (39.37inches / 1 meter) = 39,370 inches
39,370 inches x (2.54 cm / 1 inch) = 99999.8 centimeters
so, 1 km = 99999.8 cm but we need the conversion factor for cubic km and cubic cm so we cubed these conversion factors now.
(1km) ^3 = (99999.8 cm) ^3 = 1^3 km^3 = 99999.8 ^3 cm^3 = 1 km^3 = 9.99994 x 10^14 cm^3
We now use this last conversion in our original data.
(137 x 10^7 km^3) x (9.99994 x 10^14 cm^3 / 1 km) = 1.37 x 10^24 cubic centimeters
(1.37 x 10^24 cubic centimeters) x (1.03g / cubic centimeters) = 1.41 x 10^24 grams of water in the world's oceans
(1.41 x 10^24 grams) (4.184 joules / g degrees celsius) grams cancel and you are left with joules per degree celsius
= 5.90 x 10^24 joules / degree celsius. The real answer is how many joules are required to raise the temperature of one gram of water one degree Celsius, so this
answers our question. This question came from a Nivaldo Tro book that I have and the answer is not listed at the back of the book. Hope this helps.
I apologize but in the original data at the top of my answer the heat capacity should read:
(4.184 joules / (gram x degree celsius))