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A flat-plate collector has a fin-and-tube-type absorber plate. UL = 8.0 W/m²°C, the plate is 0.5 mm thick, the tube center-tube.

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Final answer:

The temperature at which the infrared heater for the sauna must run to achieve the required power output is approximately 57 Kelvin.

Step-by-step explanation:

To calculate the temperature at which an infrared heater for a sauna must run in order to achieve a required power output, we can use the Stefan-Boltzmann law of radiation. The law states that the power radiated by an object is proportional to its surface area, the Stefan-Boltzmann constant, the object's temperature raised to the fourth power, and the object's emissivity.

In this case, we are given the surface area of the heater (0.050 m²), the required power (360 W), and the emissivity (0.84). Using these values and rearranging the equation, we can solve for the temperature of the heater.

Plugging in the values:

360 W = (5.67 × 10^(-8) J/s · m² K^4) * (0.050 m²) * (T^4) * (0.84)

Simplifying the equation and solving for T:

T^4 = (360 W) / ((5.67 × 10^(-8) J/s · m² K^4) * (0.050 m²) * (0.84))

T^4 ≈ 143,489 K^4

T ≈ 57 K

Therefore, the infrared heater for the sauna must run at approximately 57 Kelvin in order to achieve the desired power output.

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