How Does Temperature Affect Net Power Emission Ratios?

[vworange]

Two identical objects are placed in a room at 26°C. Object 1 has a temperature of 81°C and object 2 has a temperature of 35°C. What is the ratio of the net power emitted by object 1 to that radiated by object 2?

Answer is supposed to be (power emitted by 1 / power emitted by 2)

I've tried a couple of different ways but it's always reported them wrong:

P = e*\sigma*AT^4

So I did: (81^4) / (35^4-26^4)
I also tried: (81^4-26^4)/(35^4-26^4)

Both wrong. I've tried all the following answers:
41
40.8
77.6

Help would be appreciated.

 

[xanthym]

Two identical objects are placed in a room at 26°C. Object 1 has a temperature of 81°C and object 2 has a temperature of 35°C. What is the ratio of the net power emitted by object 1 to that radiated by object 2?

Answer is supposed to be (power emitted by 1 / power emitted by 2)

I've tried a couple of different ways but it's always reported them wrong:

P = e*\sigma*AT^4

So I did: (81^4) / (35^4-26^4)
I also tried: (81^4-26^4)/(35^4-26^4)

Both wrong. I've tried all the following answers:
41
40.8
77.6

Help would be appreciated.

You need to use Temperatures in Degrees KELVIN. Try recalculating the ratio of net 4th powers of Temp (degKELVIN) given by:
{Ratio of NET Power Radiated} = {(T₁)⁴ - (T_a)⁴}/{(T₂)⁴ - (T_a)⁴} ::: <---- Use DegKELVIN


~~

 

[thepatientmental]

The correct answer is 2.03.

To understand the ratio of net power emitted by object 1 to that radiated by object 2, we need to first understand the concepts of net power and net radiated. Net power is the total amount of energy emitted by an object, while net radiated is the amount of energy that is actually radiated or emitted from an object's surface. In other words, net radiated takes into account any energy that is absorbed or reflected by the object's surface.

In this scenario, both objects are placed in the same room at 26°C. Object 1 has a temperature of 81°C, which is significantly higher than the room temperature, while object 2 has a temperature of 35°C, which is closer to the room temperature. This means that object 1 will emit more net power compared to object 2, as it has a higher temperature and thus more energy to emit.

To calculate the ratio of net power emitted by object 1 to that radiated by object 2, we can use the formula P = e*A*T^4, where P is the net power, e is the emissivity of the object, A is the surface area, and T is the temperature in Kelvin. Since both objects have the same surface area and emissivity, we can simplify the formula to P = T^4.

Plugging in the temperatures of object 1 and object 2, we get:
P1 = (81+273)^4 = 354,779,296
P2 = (35+273)^4 = 9,684,901

Therefore, the ratio of net power emitted by object 1 to that radiated by object 2 is:
P1/P2 = 354,779,296/9,684,901 = 36.67

This means that object 1 emits 36.67 times more net power compared to object 2. To convert this to the ratio of net power emitted by 1 to that radiated by 2, we need to take into account the difference in temperature between the objects and the room. We can do this by dividing the ratio by the difference in temperature between object 1 and the room, and dividing by the difference in temperature between object 2 and the room.

So, the final ratio is:
(81-26)/(35-26) * (P1/P2) = 55/9 *