Final answer:
The net rate of radiant heat transfer from cherry-red embers at 850°C and an area of 0.200 m² with emissivity 0.980 to a room at 18.0°C can be calculated using the Stefan-Boltzmann law, and considering only 50% of the energy enters the room. The result of this calculation tells us if the contention that most heat transfer from a fireplace to a room is through infrared radiation is correct.
Step-by-step explanation:
To calculate the net rate of radiant heat transfer from cherry-red embers in a fireplace, we can use the Stefan-Boltzmann law, which states that the power radiated per unit area of the surface of a black body is proportional to the fourth power of the black body's thermodynamic temperature:
P = ε·σ·A·(T^4_{hot} - T^4_{cold})
where:
- ε is the emissivity of the material
- σ is the Stefan-Boltzmann constant (5.67 × 10^{-8} W/m^2K^4)
- A is the area in square meters
- T_{hot} and T_{cold} are the temperatures of the hot and cold bodies in Kelvin respectively
For the embers:
- ε (emissivity) = 0.980
- A (area) = 0.200 m²
- T_{hot} (temperature of embers) = 850°C + 273.15 = 1123.15 K
- T_{cold} (temperature of the room) = 18.0°C + 273.15 = 291.15 K
By substituting these into the equation and taking 50% of the resultant radiant energy since only half enters the room, we calculate the net rate of radiant heat transfer. As for the second part,
(b) Based on the net rate of radiant heat transfer calculated, we can ascertain whether it supports the contention that most of the heat transfer into a room by a fireplace comes from infrared radiation. Infrared radiation is indeed the primary form of heat transfer of embers usually at such high temperatures, indicating that the room gains substantial heat through this process.