For earth if the observed surface temperature (K) = 288, the distance from the sun (AU) is 1.00, the albedo is .80, the Q1-5) Solar constant (Wm^-2) is 1361.0, and the Q6-10) equilibrium temperature (K) is 254 then what is the equilibrium temperature? Round to nearest whole number.


To calculate the **equilibrium temperature** of the Earth, we use the following formula for a planet's equilibrium temperature:

\[
T_e = \left( \frac{(1 - A) \cdot S}{4 \cdot \sigma} \right)^{\frac{1}{4}}
\]

Where:
- \( T_e \) is the equilibrium temperature (in Kelvin).
- \( A \) is the albedo (dimensionless).
- \( S \) is the solar constant (in \( W/m^2 \)).
- \( \sigma \) is the Stefan-Boltzmann constant, which is \( 5.67 \times 10^{-8} \, W/m^2K^4 \).

Given values:
- Albedo \( A = 0.80 \)
- Solar constant \( S = 1361 \, W/m^2 \)

Now let's calculate:

\[
T_e = \left( \frac{(1 - 0.80) \cdot 1361}{4 \cdot 5.67 \times 10^{-8}} \right)^{\frac{1}{4}}
\]

First, simplify the expression step-by-step.

I'll compute that for you.The calculated **equilibrium temperature** of the Earth, based on the given values, is approximately **186 K** (rounded to the nearest whole number).

Would you like further details on this calculation or have any additional questions?

Here are five related questions:
1. How does Earth's albedo affect its equilibrium temperature?
2. What is the significance of the solar constant in climate studies?
3. How does the actual observed surface temperature compare to the equilibrium temperature?
4. What factors could cause the equilibrium temperature to differ from the observed surface temperature?
5. How would a change in Earth's distance from the Sun affect the equilibrium temperature?

**Tip:** The equilibrium temperature is an approximation that assumes no atmosphere. Adding the greenhouse effect raises the actual surface temperature.

For earth if the observed surface temperature (K) = 288, the distance from the sun (AU) is 1.00, the albedo is .80, the Q1-5) Solar constant (Wm^-2) is 1361.0, and the Q6-10) equilibrium temperature (K) is 254 then what is the equilibrium temperature? Round to nearest whole number.

Calculate the equilibrium temperature of Earth using the Stefan-Boltzmann Law. Given an albedo of 0.80, a solar constant of 1361 W/m^2, and other planetary conditions, learn the step-by-step process to determine the equilibrium temperature. Suitable for college-level physics and planetary science students.

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