The question is as follows:

A radiating body has a Kelvin temperature , and its surroundings are at 500K (T0 >500K). If the Kelvin temperature of the radiating body is increased to 5T0, the net rate at which the body radiates increases by a factor of 14. What was the original temperature T0?

Attempt at a solution:

Using P=EPSILON*DELTA*A*(T0^4-TS^4) where T0 is temperature of the body and TS is temperature of the surroundings (i.e. 500K).

Epsilon (emmisivity), Delta (Stefan–Boltzmann constant) and A (area) can all be considered constants as they are intrinsic properties of the body which do not change.

I then called these constants a new constant B.

My two equations are now:

P=B(T0^4-TS^4)

14P=B(5T0^4-TS^4)

Isolating B in each equation and equating gives:

P/(T0^4-TS^4)=14P/(5T0^4-TS^4)

Subbing in the value for TS = 500K and working out the value for T0 keeps giving me an incorrect answer.

Most times I get an answer <500K and the only thing I got >500K was around 568K or so and this was incorrect (I have to submit online).

Any help would be appreciated.

Thanks