Radiant energy from the Sun reaches the Earth at a rate of 1.70 × 10¹⁷ W. When 30.0% of the radiant energy is reflected and 70.0% absorbed, the average temperature of the Earth's atmosphere is 253 K or −20 °C. If the atmosphere reflected 20.0% and absorbed 80.0% of the solar radiant energy, then what would be the average temperature of the Earth's atmosphere?

Question

Quizplus · Accepted Answer

First, we need to find the amount of absorbed energy by the Earth's atmosphere. 
Amount of energy absorbed = 70.0% of 1.70 × 10^17 W 
= 1.19 × 10^17 W

Then, we need to consider the reflected energy. If the atmosphere reflects 20.0% of the solar energy, then: 
Amount of energy reflected = 20.0% of 1.70 × 10^17 W 
= 0.34 × 10^17 W

The total amount of energy received by the Earth would be: 
Total energy = absorbed energy + reflected energy 
= 1.19 × 10^17 W + 0.34 × 10^17 W 
= 1.53 × 10^17 W

Now, we can use the Stefan-Boltzmann law to calculate the average temperature of the Earth's atmosphere. 
Total energy = σ × A × T^4 
where σ is the Stefan-Boltzmann constant (5.67 × 10^-8 W/m^2K^4), A is the surface area of the Earth (5.10 × 10^14 m^2) and T is the temperature in Kelvin.

So, 
1.53 × 10^17 W = (5.67 × 10^-8 W/m^2K^4) × (5.10 × 10^14 m^2) × T^4

Solving for T, we get: 
T = 261 K or -12°C

Therefore, the average temperature of the Earth's atmosphere would be -12°C if the atmosphere reflected 20.0% and absorbed 80.0% of the solar radiant energy, which corresponds to choice letter B.

Radiant Energy from the Sun Reaches the Earth at a Rate