Surface Temperature of Planet
The planet, Saturn, receives about 4.631 W/m2 from the Sun, averaged over the whole surface, and radiates an equal amount back into space (that is Saturn is in equilibrium). Assuming Saturn is a perfect emitter (e = 1.0) estimate its average surface temperature.
95.1 K
95.1 K
Approach
The intensity of the Sun's radiant energy received by the planet, Saturn, is 4.631 W/m2. Since the planet is in thermal equilibrium, this implies that the planet also radiates the same of energy back to space. For a blackbody radiator,
Q/t=e*sigme*AT^4
Q/t=e*sigme*AT^4
Solution
The Sun's intensity is equivalent to
Q/tA=I=e*sigma*T^4
Thus the temperature is
T=(Q/tAe*sigma)^0.25= (I/e*sigma)^0.25
where σ = 5.67×10-8 W/(m2·K4) is called the Stefan-Boltzmann's constant. Putting in the number gives the temperature to be 95.1 K.
Q/tA=I=e*sigma*T^4
Thus the temperature is
T=(Q/tAe*sigma)^0.25= (I/e*sigma)^0.25
where σ = 5.67×10-8 W/(m2·K4) is called the Stefan-Boltzmann's constant. Putting in the number gives the temperature to be 95.1 K.