Weihnachtsmann rot

Challenge from 2. December

Snowflake Gas

Author: Gerhard Woeginger

Project: 4TU.AMI

Challenge:

Over dinner, physics pixy Philomena tells the following story: “Today, in the physics laboratory, we performed an experiment with snowflake gas. As all of you must know, snowflake gas is an ideal gas that perfectly obeys all the mathematical laws of thermodynamics. In particular, snowflake gas satisfies the so-called ideal gas law,

p · V = kB · N · T.
In the ideal gas law,
  • p denotes the pressure of the gas,
  • V the volume,
  • N the number of particles, and
  • T the temperature.
Furthermore, the ideal gas law contains the famous Boltzmann constant
kB ≈ 1.380652 · 10-23 J/K.

Throughout the experiment, we managed to keep the amount of substance N constantly at the value …” At this moment, Philomena chokes on her food and starts coughing, so that nobody at the table gets the value of N . After recovering, Philomena fetches a diagram (as shown in the picture) from her briefcase.

Philomena explains the diagram: “Our experiment went for 8 hours. During the experiment, we continuously measured the pressure, volume, and temperature of the gas. At the beginning of the experiment, the pressure was at p0 = 8.0 bar and the volume was at V0 = 800 liter. The diagram shows the relation between the volume V and the pressure p from the beginning (A) to the end (E) of the experiment as a straight line.”

Mathematics pixy Mathilda has listened carefully to the story. Now, she says: “Okay, I get it! During the experiment, the temperatur T of the gas first started to increase. Then, after some time, the temperature reached its maximum value. From this point onwards, the temperature decreased until the end of the experiment.”

Philomena agrees: “Yes, you are right! That's exactly the way the snowflake gas behaved!”

What was the pressure p* of the gas at the time when the temperature reached its maximum value?

Artwork: Friederike Hofmann

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Possible answers:

  1. The pressure of the gas was p* ≈ 3.6 bar.

  2. The pressure of the gas was p* ≈ 4.0 bar.

  3. The pressure of the gas was p* ≈ 4.4 bar.

  4. The pressure of the gas was p* ≈ 4.8 bar.

  5. The pressure of the gas was p* ≈ 5.2 bar.

  6. The pressure of the gas was p* ≈ 5.6 bar.

  7. The pressure of the gas was p* ≈ 6.0 bar.

  8. The pressure of the gas was p* ≈ 6.4 bar.

  9. The pressure of the gas was p* ≈ 6.8 bar.

  10. The pressure of the gas was p* ≈ 7.2 bar.

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