A radiator in a domestic heating system operates at a surface temperat

In summary, the rate at which a radiator in a domestic heating system emits radiant heat per unit area, assuming it behaves as a black body, can be determined by using the Stefan-Boltzmann law and the surface temperature of the radiator, which is 55 C. The law states that radiation is proportional to the fourth power of the absolute temperature, thus the need to use (273 + 55)^4 instead of just 273 + 55. The Stefan-Boltzmann constant, 5.6697 x 10^-8, is used in the calculation.
  • #1
manal950
177
0
A radiator in a domestic heating system operates at a surface temperature of 55 C.
Determine the rate at which it emits radiant heat per unit area if it behaves as a black body ?


741333203.jpg


why we did not square the temperature
I mean ( 273 + 55)^4

please I need your help
 
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  • #2
manal950 said:
A radiator in a domestic heating system operates at a surface temperature of 55 C.
Determine the rate at which it emits radiant heat per unit area if it behaves as a black body ?


741333203.jpg


why we did not square the temperature
I mean ( 273 + 55)^4

please I need your help

Because radiation is proportional to the fourth power of the absolute temperature, not the square.

See the Stefan-Boltzmann Law:

http://en.wikipedia.org/wiki/Stefan–Boltzmann_law
 
  • #3
my question why in the answer we did not say ( ( 273 + 55)^4 ) not ( 273 + 55) without power 4
 
  • #4
Maybe same reason they did not put the right order of magnitude for the Stefan-Boltzmann constant (10^(-8) in SI units).
It may be simply some typo(s). The result seem to be OK. So they did take the fourth power to get that number.
 
  • #5
It must to make temperature with power 4 ?
 
  • #6
Yes.
 
  • #7
ok and this value 5.6697 X 10^-8 for what ?
 
  • #8
Stefan_Boltzmann constant. Did you even read about Stefan-Boltzmann law of radiation?
 

1. How does a radiator in a domestic heating system work?

A radiator in a domestic heating system works by transferring heat from hot water or steam flowing through pipes to the surrounding air. This is done through a combination of convection, where warm air rises and cool air sinks, and radiation, where heat is emitted from the surface of the radiator.

2. What is the purpose of a radiator in a domestic heating system?

The purpose of a radiator in a domestic heating system is to provide warmth and comfort to a room by heating the air. It helps to regulate the temperature in a space and can be controlled through a thermostat or by adjusting the amount of hot water or steam flowing through it.

3. What is the ideal surface temperature for a radiator in a domestic heating system?

The ideal surface temperature for a radiator in a domestic heating system can vary depending on factors such as the size and location of the room, the outside temperature, and personal comfort preferences. Generally, a surface temperature of around 140-150 degrees Fahrenheit is considered optimal for efficient and effective heating.

4. How does the surface temperature of a radiator affect its performance?

The surface temperature of a radiator directly affects its performance. If the surface temperature is too low, the radiator will not emit enough heat to warm the room. On the other hand, if the surface temperature is too high, the radiator may consume more energy and become less efficient. It is important to maintain a balanced surface temperature for optimal performance.

5. How can I ensure the surface temperature of my radiator is at the right level?

To ensure the surface temperature of your radiator is at the right level, you can use a thermometer to measure the temperature. You can also adjust the settings on your thermostat or the flow of hot water or steam to the radiator. It is recommended to consult a professional if you are unsure about adjusting the surface temperature of your radiator.

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