Physics Challenge Question 18: Solutions
Part 1
Copenhagen has average monthly temperatures between roughly 32 °F and
64 °F (a variation of 32 °F), whereas Moscow has average temperatures
ranging from 12 °F to 64 °F (a variation of 52 °F).
The reason is that Copenhagen is right on the coast. (Notice that both
cities get the same amount of heat from the sun, since they are at the same
latitude.) Since the specific heat capacity of water is so large, it takes a
long time to heat up in the summer, and a long time to cool down in the
winter.
This makes it generally true that cities with coastal climate have small
yearly temperature variations, whereas cities with inland climate have larger
temperature variations.
Another interesting reason why Scandinavia is relatively warm is a global
circulation of water called the Thermohaline Circulation, or the Ocean
Conveyor Belt. Driven by differing salt concentrations in the ocean, huge
bodies of warm water get heated up in the Pacific and Indian Oceans, and
circulate all the way north past Scandinavia, where they help keep the land
masses there warm. After cooling, the water sinks to the bottom and floats
back, completing the loop. As we know, water can store a lot of energy, so it
is also really good at “carrying” heat north to the colder areas!
Part 2
First, let’s find the mass of 1 km3 block of ice: (be careful with units here)
m    V  916.7 mkg3  1 km 3  916.7 mkg3  1  10 9 m 3  9.167  1011 kg


 


We need to add enough energy to both heat it up from –20 °C to 0 °C, and
then melt it all:
Q  mcT  mL  mcT  L
Q  9.167  1011 kg  2000 J kgC  20 C  334,000 J kg   3.43  1017 J
That is a lot of heat, most of it going to actually melt the ice.
Part 3
Let’s first find the area of the Earth covered by water. We’ll find the area
of the whole Earth (which is a sphere), and multiply it by 70% (the part
covered by water):
2
A  4r 2  0.70  4  6378 km   0.70  3.578  10 8 km 2
Knowing the base area, we can find the height of the new layer of water
from the melted ice, given that its volume is known:
V  A h
3  10 7 km 3
V
h 
 0.084 km  84 m
A 3.578  10 8 km 2
So, if all the ice in the world were to melt, much of the world’s coastal cities
would be under water. (For comparison, Boston is currently 43 m above the
sea level, and would be roughly 40 m under water if all the ice melted.)