Determination of the Lowest Possible Temperature With Arduino - the Absolute Zero Temperature

What actually is temperature? We all associate temperature with the terms hot and cold. If the temperature is high, it is hot and if the temperature is low, it is cold. But what is the physics behind the term temperature? From a physical point of view, the temperature indicates the average kinetic energy (= kinetic energy) of the particles. The formula for this is: E_kin = 3/2 * k_B * T. If the temperature T is high, the particles move faster on average and vice versa. However, the physical unit of temperature is not Celsius or Fahrenheit, but the Kelvin. If the temperature in Kelvin is doubled, the kinetic energy of the particles doubles. At T = 0K the kinetic energy of the particles is zero, i.e. they stand still. But where is this absolute zero temperature T = 0K?

For this experiment you only need the following part s:

• Arduino Nano link
• pressure sensor BMP085 or BMP180 link
• a digital thermometer link or the DS18B20 temperature sensor link
• a hollow metal sphere
• a metal suction nozzle link and a plastic one link
• Silicone tube link

You will need these Arduino-libraries: link1, link2, link3

The pressure p of a gas depends, among other things, on the temperature T. The gas law applies:

p*V = n*k_B*T

with the pressure p, the volume V, the number of particles n, the Boltzmann constant k_B and the temperature T.

In physics, a distinction is made between the following three special cases: p = constant (isobaric), V = constant (isochoric) and T = constant (isothermal).

If the pressure p is constant and only T and V can change, the gas law simplifies to V/T = constant. So doubling the temperature doubles the volume. Hot gas expands.

If the temperature T is constant and only p and V can change, the gas law simplifies to p*V = constant. Halving the volume doubles the pressure.

If the volume V is constant and only p and T change, the gas law simplifies to p/T = constant. A doubling of temperature causes a doubling of pressure, or as in our experiment, a decrease in temperature causes a decrease in pressure. This case is called isochoric and the corresponding law p/T = constant is called Gay-Lussac-law named after the physician Joseph Louis Gay-Lussac (1778 - 1850).

So if you leave the volume V constant and only change the temperature T and the pressure p, you get a straight line p = constant * T. As the temperature T decreases, the pressure p also decreases.

And now what is special about this law: When the temperature approaches absolute zero temperature T = 0 K, the pressure p also becomes 0. So if you now determine the pressure p for different temperatures T, you only have to extend the straight line until the pressure p equals 0. The temperature T determined in this way is then the absolute zero temperature.

The experiment to determine absolute zero temperature is very simple. You put the metal ball in a pot with water and heat it to 100 °C. The metal ball is connected to the pressure sensor with a hose. For this purpose you will need to glue a plastic hose connector on the pressure sensor. Be careful not to cover the sensor-hole with glue! Then you let the water cool down slowly and determine the respective pressure p for the different temperatures. Finally, draw the graph p = p(T). You should get approximately a straight line.

If you now extend this to the left in the direction of a lower temperature, the pressure p is 0 bar at a certain temperature. This temperature is then exactly the absolute zero temperature. In my measurement it is around -290°C. The correct value is -273.15°C = 0 K. So you have experimentally determined the lowest possible temperature, congratulations!

As we have seen in this experiment, there is a lowest temperature T, namely absolute zero. This can even be determined very easily using the Gay-Lussac law. However, there is no maximum temperature T, because the kinetic energy of the particles and thus their temperature can increase indefinitely. For example, in the corona of our sun, this is the outer atmosphere of a star, temperatures of several million Kelvin prevail! We on earth already sweat a lot at 40°C. If you want to see more exciting physics experiments, here is my homepage and my Youtube channel:

Homepage

Youtube-channel

In this sense, have fun experimenting and Eureka!