I saw a documentary that claimed melting polar ice caps are causing sea levels to rise. Something was fishy about that claim so I made some simplifying assumptions, drew a free body diagram and started doing algebra. I won't reproduce the algebra here because it turns out there is a common sense way to reach the same conclusion.
Simplifying assumptions
- No saltwater
- Ice is pure water
- Ice is free-floating
- No condensation
- No evaporation
Free body diagram
not drawn to scale
Common sense
Since the system is in equilibrium the buoyancy force (red) is equal in magnitude to the gravitational force (blue).
Under the force of gravity the ice will displace some volume of water. The mass
of the displaced volume of water must be equal to the mass of the ice causing
that water to be displaced. Therefore, the water from the melted ice has the
same volume as the water originally displaced! The water level will not change!
Wait a minute! How do we know that The mass of the displaced volume of water
must be equal to the mass of the ice causing that water to be displaced.?
Well, picture this: gravity is applying to a body of water. Pushing against the
water causes an equal-magnitude and opposite-direction reaction. The more water
is displaced the greater reaction force. You are pushing against gravity!
This is the buoyancy force!
The force an object can exert due to gravity on a body of water is determined by its mass. That object will sink if the force exerted by the object is greater than the buoyant force. In other words: if the mass of the object is greater than the mass of the object's volume in water then the object sinks.
If the mass of an object is less than the mass of the object's volume in water... then the object floats.
In other words, objects denser than water sink, objects less dense than water float.
Back to saltwater
In the previous discussion the medium of floatation was the same as the object of displacement. In other words: ice (frozen H2O) is floating in water (liquid H2O). Obviously, once the ice melts it's all water with the same properties, including density.
So what happens to the fluid level when ice (frozen H2O) floating in saltwater melts?
I leave this as an exercise for the reader.