Two identical objects are placed in a room with a temperature of 20°C.Object A has a temperature of 50°C,while object B has a temperature of 90°C.What is the ratio of the net power emitted by object B to the power emitted by object A?
A)1.7
B)2.8
C)81
D)17
E)21

Question

Quizplus · Accepted Answer

The net power emitted by an object due to thermal radiation can be calculated using the Stefan-Boltzmann law, which states that the power emitted is proportional to the fourth power of the absolute temperature (in Kelvin). The formula for power emitted by an object is $P = \sigma A (T^4 - T_0^4)$, where $\sigma$ is the Stefan-Boltzmann constant, $A$ is the surface area of the object, $T$ is the temperature of the object, and $T_0$ is the temperature of the surroundings. Since both objects are identical and placed in the same environment, $A$, $\sigma$, and $T_0$ are constants for both objects. Therefore, the ratio of the net power emitted by object B to that of object A is given by the ratio of their temperatures to the fourth power, subtracting the fourth power of the room temperature in each case.Let's convert the temperatures to Kelvin by adding 273 to each:- Object A: $50°C = 323K$- Object B: $90°C = 363K$- Room temperature: $20°C = 293K$The ratio of the net power emitted is then:$$\frac{P_B}{P_A} = \frac{(363K)^4 - (293K)^4}{(323K)^4 - (293K)^4}$$Calculating this ratio gives a value close to 2.8, making option B the correct answer.

Two Identical Objects Are Placed in a Room with a Temperature