# Temperature given ratio of power out/power in

1. Nov 19, 2009

### elmers2424

Statement: If Jupiter emitted just as much energy per second (as infared radiation) as it receives from the Sun, the average temperature of the planet’s cloud tops would be about107 K. Given that Jupiter actually emits approximately twice this much energy per second, calculate what the average temperature must actually be.

I am given an example that T(Jup.) = 103 K, the temperature of the planet as a total blackbody is T = 127 K, and therefore [T(observed)/T(calculated)] ^ 4 = Power out/ Power in

In this specific example then, I have... [127/103]^4 = 2.3 which means that Jupiter emits 2.3 times the power than it absorbs

How am supposed to go about this problem. First, I thought that if I make Tcalc = 107 K and set (Tobs./107)^4 = 1 (from the first part of the statement), then I can calculate Tobs. and use it. This would mean that To must be 107 too.

Then, if I plug (107/Tcalc)^4 = 2 (for twice as much energy/s) my Tcalc will come out to approximately 90K.

Is this all i need to do? 90K does not seem right to me. Suggestions would help me tremendously! Thanks