How to Calculate the Temperature Needed for an Infrared Heater in a Sauna?

What temperature must the infrared heater for a sauna run at if the required power is 331 watts?

Given data:

Surface area: 0.05 m²

Emissivity: 0.8

Required power: 331 watts

Answer:

Using the Stefan-Boltzmann law of radiation, we can calculate that the infrared heater for the sauna should run at a temperature of approximately 855.8 Kelvin to produce a power output of 331 watts.

To solve this physics problem, we should use the Stefan-Boltzmann law of radiation that asserts, P = σeAT^4, where P is power, σ is the Stefan-Boltzmann constant (5.67 × 10^-8 J/s.m².K^4), e is the emissivity, A is the surface area, and T is the absolute temperature in Kelvin. The power provided in the problem is 331 watts, the emissivity (e) of the infrared heater for the sauna is 0.8, and the surface area (A) is 0.05m².

Plugging these values into the equation, we can solve for T. So, our equation becomes 331 W = (5.67 × 10^-8 J/s. m². K^4) × 0.8 × 0.05m² × T^4. Solving for T, we find that the temperature of the heater should be around 855.8 Kelvin.

The Stefan-Boltzmann law of radiation is an essential formula in physics that helps in determining the temperature needed for various radiative processes. By understanding this law, we can calculate the temperature for infrared heaters, stars, and other radiation-emitting objects.