The volume of the earth’s oceans is around 1.35 billion cubic kilometers or 1.35×1018m3. Mass of salt water is around 1030kg/m3.
The specific heat capacity of sea water is 3930J/kg/K.
Thus the amount of energy required to heat the oceans for each 1C change is:
E = 1.35×1018m3 x 1030kg/m3 x 3930J/kg/K. = 5.46×1024J/K
71% of our planet is ocean and the planet’s surface area is 5.10×1014m2
so, if 1W of energy were arriving on every 1m2 of planet surface, then if this were all evenly distributed in the ocean, (ignoring heat losses) the time to increase the temperature of the whole ocean by 1C is:
Time = 1C x 5.46×1024J/K / (1W x 0.71 x 5.10×1014 ) = 1.51×1010
Time = 478years
In other words, if W is the power per unit area, then the rate of temperature rise is given by:
Temp rise of ocean per year = Watts per unit meter / 478
Or turning around
Time = 478 x Temperature rise / Power per unit meter
Thus to answer the obviously silly question:
“how long does it take to boil the oceans”.
Assuming an average temperature around 4C and an increase in power of 4w/m2 (around that usually cited for CO2 warming), the time taken is:
Time = 478 x (100-4) / 4 = 11,500 years