## 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****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.