Question

The estimated current overall average temperature of the planet Earth is 15 degrees C. If the planet were to increase in temperature by 2 degrees C (the goal of the Paris Climate Accord of 2015), how much additional energy would be radiated from the planet (in Watts) and what percent increase would this be? (Hint: Radius= 6,367 km).

Please show work and explanation if possible, as to I am slow, and takes time for me to understand.

Thank you

Answer 1

Heat transfer by radiation

Q = A (T⁴)

Stefan Boltzmann constant = 5.67 x 10^-8 W/m2-K4

Area A = 4 x 3.14 x R²

= 4 x 3.14 x (6367 km x 1000m/km)²

= 5.092 x 10^14 m2

T1 = 15 + 273 = 288 K

T2 = 17 + 273 = 290 K

Q1 = A (T1⁴)

Q1 = 5.67 x 10^-8 x 5.092 x 10^14 x (288⁴)

Q1 = 5.67 x 10^-8 x 5.092 x 10^14 x (6879707136)

Q1 = 1.986 x 10^17 W

Q2 = A (T2⁴)

Q2 = 5.67 x 10^-8 x 5.092 x 10^14 x (290⁴)

Q2 = 5.67 x 10^-8 x 5.092 x 10^14 x (7072810000)

Q2 = 2.042 x 10^17 W

Additional energy radiated = Q2 - Q1

= (2.042 x 10^17) - (1.986 x 10^17)

Q = 5.6 x 10^15 W

% increase = Q x 100 / Q1

= 5.6 x 10^15 x 100 / (1.986 x 10^17)

= 2.82 %