# Calculating Power at the Focal Point with Temperature Measurements

• Z0rb
In summary, a new member of the forum is seeking help in determining the power of a small Fresnel lens. After some initial calculations and assumptions, it is estimated to be around 9 watts, but more accurate measurements are desired. Suggestions are made to conduct an experiment using a known volume of water instead of directly measuring with a thermocouple.
Z0rb
Hello All,

I am new to this forum, and right up front I will say I know very little about physics in general. That does not however limit my ability to question and ask for help from people in the know.

Here is my dilemma. I have a small Fresnel lens approx. 6 cm X 15 cm. Or 90 square centimeters. I would like to know how much power in Watts this is really focusing.

I did a little math under the assumption of each square meter receiving 1000 Watts of solar energy on a sunny day at the equator and came up with about 9 watts of calculated power at the focal point.

This of course is a figure that assumes there is no loss in the system. So to get a better idea of how much power is REALLY at the focal point, I want to make some measurements.

I have a K-Type thermocouple hooked into a meter that can read up to 750 degrees Celsius with moderate accuracy. I’ll place the thermocouple at the focal point. The focal point appears to be about 1 cm in diameter. The diameter of the thermocouple is about half of that.

Is it possible (and if so can I have it explained to me), to calculate how much wattage is at the focal point, by taking a temperature reading over time?

Any help or explanation would be great.

Thanks

Your initial assumption is reasonable- 9 watts. For more accuracy, you need the right tools, and a thermocouple is not it.

Even so, you have the beginnings of an interesting experiment- the power will depend on the atmospheric conditions (air absorption), and since you have some tools, why not do the experiment and see what happens?

However, I would instead focus the light into a (known) volume of water into which the thermocouple is inserted, rather than directly onto the thermocouple. That will give you better stability and accuracy.

for your question. Calculating the power at the focal point of your Fresnel lens using temperature measurements is possible, but it will require some additional information.

First, you will need to know the specific heat capacity of the material that your lens is made of. This is a measure of how much energy is needed to raise the temperature of a certain amount of the material by one degree.

Next, you will need to measure the change in temperature over a certain amount of time at the focal point. This will give you the change in energy (in joules) at the focal point.

Using the specific heat capacity, you can then calculate the amount of energy in joules that is needed to raise the temperature of the thermocouple by the measured amount. This will give you the power (in watts) at the focal point.

However, keep in mind that this calculation will only give you an approximation of the actual power at the focal point. Factors such as losses in the system, efficiency of the lens, and other variables may affect the accuracy of your calculation. It would be best to repeat the measurement multiple times and take an average to get a more accurate result.

I hope this helps and good luck with your experiment!

## 1. How do you calculate power at the focal point with temperature measurements?

The power at the focal point can be calculated by using the formula: P = (C0 x ΔT) / τ where P is the power, C0 is the specific heat capacity, ΔT is the change in temperature, and τ is the time taken for the temperature change to occur.

## 2. What is the significance of measuring temperature when calculating power at the focal point?

Measuring temperature is essential in calculating power at the focal point because it helps determine the change in thermal energy, which is necessary for the formula to accurately calculate power.

## 3. How can temperature measurements be taken at the focal point?

Temperature measurements can be taken at the focal point using a thermometer or a thermal imaging camera. The thermometer is placed at the focal point, and the temperature is recorded. The thermal imaging camera can capture the temperature distribution at the focal point.

## 4. What factors can affect the accuracy of power calculation at the focal point using temperature measurements?

Some factors that can affect the accuracy of power calculation at the focal point include environmental conditions, such as air currents or external heat sources, as well as the quality and calibration of the temperature measuring device.

## 5. Are there any limitations to calculating power at the focal point with temperature measurements?

Yes, there are some limitations to this method. The accuracy of the measurement can be affected by the material properties of the object being heated, as well as the size and shape of the focal point. Additionally, this method may not be suitable for highly reflective or transparent materials, as they can affect the temperature readings.

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