Final answer:
The rate of radiant heat transfer from the fireplace can be calculated using the Stefan-Boltzmann law, considering the emissivity, area, and temperature difference between embers and the room.
Only 50% of this energy enters the room as heat, from which the net rate can be calculated in kilowatts. This supports the contention that infrared radiation is a significant mode of heat transfer from the fireplace.
Step-by-step explanation:
To answer this question, we must apply the concept of radiant heat transfer. Using the Stefan-Boltzmann law, the rate of energy emission from the cherry-red embers can be calculated using the formula: Power (P) = emissivity (ε) * Stefan-Boltzmann constant (σ) * Area (A) * (Temperature4 - Temperatureenvironment4). We have been given the emissivity of the embers as 0.980, the area as 0.200 m2, the temperature of the embers as 850°C (which must be converted to Kelvins), and the room temperature as 18.0°C (also converted to Kelvins).
First, convert the temperatures to Kelvins:
Temperature of embers = 850 + 273.15 = 1123.15 K
Temperature of room = 18 + 273.15 = 291.15 K
Then, plug in the values into the Stefan-Boltzmann law equation:
P = 0.980 * 5.6703 x 10-8 W/m2K4 * 0.200 m2 * ((1123.154) - (291.154))
This will give us the rate at which heat is radiated by the embers. Since only 50% of the radiant energy enters the room, you would then find 50% of that total emission. The result is the net rate of radiant heat transfer that would be calculated in kilowatts (kW).
Part (b) of the question asks if this supports the contention that most of the heat transfer into a room by a fireplace comes from infrared radiation. Without the exact numerical calculations given here, the premise is that a significant portion of energy transfer from a fireplace is indeed through infrared radiation, as the embers radiate heat at a high temperature. The detailed calculations will illustrate the significance of this heat transfer in comparison to other forms of heat transfer such as conduction or convection.