I saw this science chart showing that oceans are gaining massive amounts of heat. Will this cause them to boil away?
Short answer: Because the oceans are massive and massive amounts of heat are needed to change them. Relative to the size of the oceans the warming is trivial.
Long answer: First we need to know how much oceans are warming. One NOAA chart I saw showed about an 180 ZJ rise in 30 years. That works out at 6 ZJ/year. [1 ZJ = 10²¹ joule]
Next we need to know how much ocean there is. Total mass of water on the earth's surface = 1.35 × 10²¹ kg, almost all of it ocean.
That conveniently works at at 6 J per 1.35 kg of water, because 1 ZJ = 10²¹ J. Which works to be 4.444 J per kg of water.
How will that much heat affect water?
Adding energy to water will increase its temperature. To find out by how much, we need to know the heat capacity of water. Heat capacity is the amount of heat needed to raise the temperature by 1 ºC.
The heat capacity of water = 3993 J/kg/K, which means 3993 joules of energy will raise the temperature of one kilogram of water by one degree celsius.
The find out the number of years, needed to raise the temperature of all the water on earth by 1 ºC, we divide 3993 by 4.444. That is 898½ years. So currently the average ocean temperature increase is about 0.0011 ºC per year. In 898 years time, oceans could be 1 ºC warmer at this rate. Or, the next deep glaciation may be well be underway by then, and oceans may have started cooling.