Answer:
To calculate the greenhouse effect required for the Earth's temperature to increase from 239 K to 288 K, we need to consider the difference in temperature and the role of greenhouse gases in trapping heat.
The greenhouse effect is the process by which certain gases in the Earth's atmosphere trap and re-radiate heat, thus keeping the planet warmer than it would be without an atmosphere. Greenhouse gases include carbon dioxide (CO2), methane (CH4), and water vapor (H2O).
To calculate the greenhouse effect, we can consider the energy balance equation:
Incoming Solar Radiation = Outgoing Thermal Radiation + Greenhouse Effect
In this case, the incoming solar radiation is balanced by the outgoing thermal radiation and the greenhouse effect. Since the greenhouse effect is responsible for the additional warming beyond what can be explained by outgoing thermal radiation alone, we can determine the greenhouse effect as:
Greenhouse Effect = Incoming Solar Radiation - Outgoing Thermal Radiation
The incoming solar radiation can be estimated as the solar constant, which is approximately 1361 watts per square meter (W/m²).
The outgoing thermal radiation can be estimated using the Stefan-Boltzmann law, which states that the energy radiated by a black body (in this case, the Earth) is proportional to the fourth power of its temperature:
Outgoing Thermal Radiation ∝ Temperature^4
Using these equations, we can calculate the greenhouse effect:
Greenhouse Effect = Incoming Solar Radiation - Outgoing Thermal Radiation
= 1361 W/m² - (Temperature^4 * σ)
where σ is the Stefan-Boltzmann constant (approximately 5.67 x 10^-8 W/(m²K^4)).
Substituting the initial and final temperatures, we get:
Greenhouse Effect = 1361 W/m² - (288 K^4 * σ) - (239 K^4 * σ)
Calculating the values and subtracting them will give us the greenhouse effect required for the temperature increase from 239 K to 288 K.