A brass rod radiates energy at the rate of 10 watt at 100°C. If temperature is increased to 200°C, at what rate does it radiate now?

Radiative energy loss is proportional to the 4th power of absolute temperature.
In the first condition, absolute temperature is
  100 + 273.15 = 373.15 Kelvin
In the second condition, absolute temperature is
  200 + 273.15 = 473.15 Kelvin
The 4th power of the ratio is
  (473.15/373.15)^4 = 1.268^4 = 2.585

At the higher temperature, the rod will radiate (10W)*2.585 = 25.85 watts.