The Earth intercepts 1.27 × 10¹⁷ W of radiant energy from the Sun. Suppose the Earth, of volume 1.08 × 10²¹ m³, was composed of water. How long would it take for the Earth at 0°C to reach 100°C, if none of the energy was radiated or reflected back out into space?

Question

Quizplus · Accepted Answer

To calculate the time, use the formula Q = mcΔT, where Q is the energy required, m is the mass, c is the specific heat capacity of water, and ΔT is the temperature change. The mass of the Earth if it were water is its volume times the density of water (1.08 × 10^21 m^3 × 1000 kg/m^3). The specific heat capacity of water is 4,186 J/kg°C, and ΔT is 100°C. Calculate Q and divide by the power intercepted (1.27 × 10^17 W) to find the time.

The Earth Intercepts 1