A lamp radiates 75. J/s when the room is set on 27°C but it radiates 90. J/s when the room temperature drops to 10. C. What is the temperature of the lamp?

Question

Quizplus · Accepted Answer

The lamp radiates more energy when the room temperature is lower, which means that the lamp is hotter than the room. The difference in radiation between the two temperatures is 90 J/s - 75 J/s = 15 J/s. This difference is due to the Stefan-Boltzmann law, which states that the power radiated by a blackbody is proportional to the fourth power of its temperature. Therefore, the ratio of the temperatures of the lamp and the room is equal to the fourth root of the ratio of their radiated powers. In this case, the ratio of the temperatures is equal to the fourth root of (90 J/s / 75 J/s) = 1.14. Therefore, the temperature of the lamp is 1.14 times the room temperature, which is 27°C * 1.14 = 30.78°C.

A Lamp Radiates 75