A Feel for Thermodynamics.
Thermodynamics is a well-founded branch of Science because it is based on experiments and "thought experiments". Thermodynamics comes into Physics, Chemistry, Chemical Engineering, Biology and many other Sciences including COSMOLOGY.
I would like my readers to get a "feel for Thermodynamics".
To obtain this degree of understanding you need practical experience. Compare this with learning to play the violin, you cannot learn to play the violin by studying the theory of vibrating strings and the theory of obtaining a higher pitch by shortening the string. You must do a lot of practice.
So let us consider a practical experiment. What happens when air is let out of the spare tyre of your car ? Does the temperature of the air fall because the air has expanded ? Pump air into the tyre to a practical high pressure and then leave the tyre in a corner of your garage for a sufficient time for the temperature of the tyre reach equilibrium with the surroundings. Measure that temperature with a thermometer. Now let air out of the tyre and measure the air temperature. (Make sure that the thermometer bulb is not wet, because the evaporation of moisture will lower the temperature). You will find that the temperature is almost constant, BUT DON'T TAKE MY WORD FOR IT - TRY IT YOURSELF.
Actually there is a small drop in temperature due to the Joule-Thomson Effect.
Now cosmologists such as D. Sciama, P.C.W. Davies and others use this equation to describe the fall in temperature of a freely expanding gas -
TVg - 1 = constant.
In the case of air, g = 1.4
therefore g - 1 = 0.4
Therefore an increase of volume by a factor of 3 (for example) should reduce the temperature by a factor of 0.64 - i.e. from 200 C (293 K) to - 840 C (189 K).
So your experiment has proved that the equation which cosmologists use for calculating the fall in temperature of the expanding Universe is wrong!
The errors which have crept into Cosmology have come about because most cosmologists are mathematicians and theoretical physicists who have no practical experience in Thermodynamics.