# Calculating Laser Power from Temperature Rise, Time, and Target Mass?

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## Main Question or Discussion Point

Hi Everyone!

There is a type of CO2 laser cutter power meter on the market (Product link removed)

The meter uses a block of black anodized aluminum bonded to the end of basically a mechanical meat thermometer, and has a zero adjustment on the back of the face to set the base temperature to room temperature, and a reskinned dial that indicates the temperature as watts.

To use it, you shine the laser's defocused beam onto the target for a prescribed number of seconds as indicated on the calibration tag on each meter (such as "37.7 seconds"), then turn the laser off. You then watch the meter to see how high the indicator needle travels as it will continue to rise, and the peak is your wattage reading for the laser's power.

What's the math behind the calculation that this meter uses to calculate the wattage of the laser's beam?

I'm guessing that IF you know

o Mass of the target body
o Time of energy imparted on the target
o Temperature rise over the interval of time

then you can calculate the watts that have been imparted on the target.

Am I correct in this guess?

What would the equation be for this?

Also, how would you adjust the equation to handle how much the target absorbs or reflects the energy from the laser (for example, if you used anodized aluminum for the target versus other materials)?

Thank you very much!

--Jim

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DrClaude
Mentor
The base equation is simply the equation for heat capacity:
$$C = \frac{Q}{\Delta T}$$
Knowing $C$ for the block and measuring $\Delta T$, you can then get the power by $Q/\Delta t$. But...

As you said, this is far what will happen in real life. The actual amount of heat $Q$ transferred will depend, among others, on the absorptivity of the block at the wavelength of the laser. It is also quite possibly non-linear for high-power cases. You also have to account for heat loss while waiting for the thermometer to stabilise.

My guess is that the only way to do it with any reasonable accuracy is by calibration, sending pulses from lasers with known power and measuring the corresponding change in temperature.

The base equation is simply the equation for heat capacity:
$$C = \frac{Q}{\Delta T}$$
Knowing $C$ for the block and measuring $\Delta T$, you can then get the power by $Q/\Delta t$. But...

As you said, this is far what will happen in real life. The actual amount of heat $Q$ transferred will depend, among others, on the absorptivity of the block at the wavelength of the laser. It is also quite possibly non-linear for high-power cases. You also have to account for heat loss while waiting for the thermometer to stabilise.

My guess is that the only way to do it with any reasonable accuracy is by calibration, sending pulses from lasers with known power and measuring the corresponding change in temperature.
Hi Dr. Claude...

Wow, thank you very much for this info!

So I did some experiments tonight with a 10mm cube of anodized aluminum, and noticed that with full laser power focused on the cube, the cube temperature would stabilize within about 90 seconds at a maximum temperature of about 350 degrees C on my laser cutter.

Is there a way to deduce an equation from this info?

Thanks!

DrClaude
Mentor
Is there a way to deduce an equation from this info?
Far from an expert on this, but I don't think you can get any reasonable number without calibration.

Hi DrClaude...

I totally agree! That's what I will try.

Thank you very much for helping me onto the right path!