A room is heated by a radiator that has a constant temperature T (unknown). When the outside temperature is 260 K, the room temperature is 300 K. However, when the outside temperature drops to 240 K, the room temperature is only 290 K. Estimate the radiator temperature T.

Answer

`340`

Explanation

The rate of the heat transfer is approximately proportional to the temperature difference, between radiator and room as well as between the room and he outside. The corresponding proportionality constants can be denoted as C ("radiator-room") and D ("room-outside") Then, intially,
`C(T-300)=D(300-260)`
For the second set of temperatures:
`C(T-290)=D(290-240)`
Solving the equations yields T=340 K