Problem 118P

Global warming refers to the rise in average global temperature due to the increased concentration of certain gases, called greenhouse gases, in our atmosphere. Earth's oceans, because of their high heat capacity, absorb heat and therefore act to slow down global warming. How much heat would be required to warm Earth's oceans by 1.0 °C? Assume that the volume of water in Earth's oceans is 137 × 107 km3 and that the density of seawater is 1.03 g/cm3. Also assume that the heat capacity of seawater is the same as that of water.

Solution 118P

We calculate temperature change due to heat transfer with this equation:

Q = m x c x delta T

Where Q stands for the energy transferred, m is the mass of the material, c is the specific heat capacity of the material, and delta T is the change in temperature.

In this case, c = 4.186 joules per gram per degree C

Delta T = 1

We need to calculate the mass of the oceans in grams for m

1 Km = 1 x 10^5 cm; we cube this to get:

1 Km^3 = 1 x 10^15 cm^3

Then we can do the conversion -

137 x 10^7 Km^3 x 1 x 10^15 cm^3/1 Km^3 = 1.37x10^24

Now, back to Q = m X c X delta T

Q = 1.37x10^24 x 4.186 x 1

Q = 5.735x10^24 Joules