To get an idea of how much thermal energy is contained in the world's oceans, estimate the heat liberated when a cube of ocean water, 3 km on each side, is cooled by 4 K. (Approximate the ocean water as pure water for this estimate.)

Q = 4.52 10¹⁷ J

Explanation:

Thermal energy can be calculated with  

      Q = m c_{e} ΔT

in this case it indicates that we approximate seawater to pure water with  

    c_{e} = 4186 J/ kg K  

with the density

    ρ = m / V  

    m = ρ V  

    V = L³  

we substitute  

   m = ρ L³  

   Q = ρ L3 c_{e} ΔT

calculate  

   Q = 1000 (3 103) 3 4186 4  

   Q = 4.52 10¹⁷ J

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2