Two identical objects are in the same surroundings at 4.50oC. One is at a temperature of 1400 K, and the other is at 1040 K. Find the ratio of the net power emitted by the hotter object to the net power emitted by the cooler object.
To find the ratio of the net power emitted by the hotter object to the net power emitted by the cooler object, we can use the Stefan-Boltzmann law. According to the Stefan-Boltzmann law, the power emitted by an object is directly proportional to its temperature raised to the fourth power.
The formula for the power emitted by an object is given by:
P = σ * A * T^4
Where:
P is the power emitted by the object,
σ is the Stefan-Boltzmann constant (approximately equal to 5.67 × 10^-8 W⋅m^-2⋅K^-4),
A is the surface area of the object,
T is the temperature of the object.
Since the two objects are identical, they have the same surface area (A). We can omit the surface area from our calculations as it cancels out when we calculate the ratio of their powers.
Let's denote the temperature of the hotter object as T1 (1400 K) and the temperature of the cooler object as T2 (1040 K).
The ratio of their powers emitted can be calculated as:
P1/P2 = (σ * T1^4) / (σ * T2^4)
P1/P2 = (T1/T2)^4
P1/P2 = (1400 K / 1040 K) ^ 4
Now, we can calculate the ratio of their net powers emitted:
P1/P2 = (1.346)^4
P1/P2 ≈ 3.03
Therefore, the ratio of the net power emitted by the hotter object to the net power emitted by the cooler object is approximately 3.03.