When people think of global warming, they often think of hotter summers and the

Question

When people think of global warming, they often think of hotter summers and the
melting of ice sheets. However, is global warming really an ocean warming problem?
Note that the top 100m of the ocean is well-mixed, i.e., heating at the surface is easily
distributed through the top 100m of the ocean by wave breaking and other mixing
processes. Given this, calculate
(a) How much energy is needed to heat the standard atmosphere by 1 degree
Celsius? Assume you are heating a column of air with a base of 1 square
meter.
(b) How much energy is needed to heat the surface mixed layer of the ocean by
1 degree Celsius? Again, assume you are heating a column of water with a
base of 1 square meter.

(c) How much more (or less) heat capacity is there in the ocean? Express your
answer as a ratio. Is most of the world's warming being captured by the
ocean or by the atmosphere?

Explanation / Answer

a) for solving this problem, we will need some properties of air, like air density and heat capacity Cp value of air. Assuming air temperature as 30C, we will take the coresponding value of air at 30C.

So, at 30C, the density og air = 1.1644 kg/M3

Specific Heat of Air at 30 C Cp = 1.005 Kj/KgK

So, assuming the column area of air is 1m2 and taking 100 metre height,

The total volume of air V = 1X100 = 100m3

So, mass of this air m = 100X1.1644 = 116.44Kg

So heat required to heat this air by 1deg = mCpX(T2-T1) = 116.44X1.005X1 = 117 kiloJoule ANS

b) In this case we are heating a water column of same volume, as base area is same. But here the density and Cp value will be different. The density of water is 996kg/m3 and Cp value is 4.18Kj/KgK

So heat required to Heat the water column = VXdXCpX1 = 100X996X4.18X1= 416328 KJ ANS

c) So ratio of heat capacity of water to air = 416328/117 = 3558.36

So, the world's most of the warming is captured by atmosphere not by Ocean as Ocean requires much much more heat to increase its temperature.

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