By what factor does the rate of radiant emission of heat, from a heating element, increases when the temperature of a heating element increases from 27oC to 327 oC?
To calculate the factor by which the rate of radiant emission of heat increases when the temperature of a heating element increases, we need to use the Stefan-Boltzmann Law. This law states that the power P radiated per unit area by a blackbody is proportional to the fourth power of its absolute temperature.
The equation for the Stefan-Boltzmann Law is:
P = σ * A * T^4
Where:
P is the power radiated
σ is the Stefan-Boltzmann constant (approximately 5.67 × 10^-8 W/m^2K^4)
A is the surface area of the heating element
T is the absolute temperature of the heating element
We need to compare the power radiated at two different temperatures, T1 (27°C) and T2 (327°C). First, we convert the temperatures to Kelvin by adding 273 to each value:
T1 = 27 + 273 = 300 K
T2 = 327 + 273 = 600 K
Now we can calculate the ratio of the power at T2 to the power at T1:
P2/P1 = (σ * A * T2^4) / (σ * A * T1^4)
= (T2 / T1)^4
Substituting the temperature values:
P2/P1 = (600 K / 300 K)^4
= 2^4
= 16
Therefore, the rate of radiant emission of heat from the heating element increases by a factor of 16 when the temperature increases from 27°C to 327°C.