What is the emissivity of a stainless steel tank based on the given infrared thermometer reading?
Question:
An infrared thermometer calibrated for emissivity of 0.95 gives a reading of 34°C for a stainless steel water heater with boiling water. What is the emissivity of this stainless steel tank?
Answer:
The emissivity of the stainless steel tank is 0.95.
To determine the emissivity of the stainless steel tank, we can use the given information and the fact that the infrared thermometer is calibrated for an emissivity of 0.95.
First, let's understand how the infrared thermometer works. It measures the thermal radiation emitted by an object and uses this information to calculate its temperature. The thermometer is calibrated for a specific emissivity value, which is the ratio of the object's actual thermal radiation to the thermal radiation emitted by a perfect black body at the same temperature.
In this case, the infrared thermometer gives a reading of 34°C for the stainless steel water heater with boiling water. This reading is based on an emissivity value of 0.95, which means that the stainless steel tank is emitting thermal radiation equivalent to 95% of a perfect black body at the same temperature.
To find the emissivity of the stainless steel tank, we can set up the following equation:
Emissivity x Thermal radiation of stainless steel tank = Thermal radiation of perfect black body
Since the thermometer reading is based on an emissivity of 0.95, we can substitute the values into the equation:
0.95 x Thermal radiation of stainless steel tank = Thermal radiation of perfect black body
Since the boiling water in the stainless steel tank is at its maximum temperature, it is equivalent to the temperature of the perfect black body. Therefore, the thermal radiation of the perfect black body is equal to the thermal radiation of the stainless steel tank.
Simplifying the equation, we have:
0.95 x Thermal radiation of stainless steel tank = Thermal radiation of stainless steel tank
Dividing both sides of the equation by the thermal radiation of stainless steel tank, we get:
0.95 = 1
Therefore, the emissivity of the stainless steel tank is 0.95.