How to Calculate the Temperature for an Infrared Heater?
What temperature should an infrared heater run at if the required power is 332 W?
Can you explain how to determine the temperature of an infrared heater based on the given power and surface area?
Temperature Calculation for Infrared Heater
To calculate the temperature at which an infrared heater must run based on the required power of 332 W, we can use the Stefan-Boltzmann law formula.
Understanding the Stefan-Boltzmann Law:The Stefan-Boltzmann law states that the power radiated per unit surface area is directly proportional to the fourth power of the absolute temperature of the surface and its emissivity. Mathematically, the formula can be expressed as:
P/A = σεT^4
Where: - P represents the power radiated - A is the surface area - σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2·K^4) - ε is the emissivity - T is the absolute temperature of the surface
Calculating the Temperature:By rearranging the equation and substituting the provided values, we can calculate the temperature of the infrared heater using the formula T = (P/(Aσε))^(1/4).
Substitute the values into the equation:
T = (332/(0.05 x 5.67 x 10^-8 x 0.88))^(1/4)
By solving the equation, we find that the temperature T is approximately equal to 475 K. Therefore, the infrared heater must run at a temperature of around 475 K to achieve the required power output of 332 W.