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I made an experiment using a closed syringe with the volume marks. At the beginning, the piston is at $5\rm\, ml$, then I move it to $20\rm\, ml$.

Since the change is approximately adiabatic, we can use the adiabatic expressions, one of them being $$TV^{\gamma-1}=\text{const.}$$ For $T_1=20°C=293.15\rm\, K$, $V_1=5\rm\, ml$, and $V_2=20\rm\, ml$, $$T_2=T_1\frac{V_1^{\gamma-1}}{V_2^{\gamma-1}}=168.4\rm\, K = -104.8°C$$ Such a drastic drop should be rather sensible. However, I haven't felt anything.

Was my setup wrong? Is the change not adiabatic? Have I set the equations incorrectly?


Explicit data for sake of comments:

  • Gas used is just ordinary air: at the beginning it is at standard pressure.
  • I didn't use any thermometer; according to the 0th law of termodynamics, I expected that the (in theory) cooled air should take away heat from my skin. In fact, the gas at $\approx -100°C$ should be destructive to my skin, but my finger is still intact, therefore my theory is wrong.
  • Syringe can be thought of as an ideal conductor. Its thickness is less than $1\rm\, mm$, hence it can be neglected. As said, the low temperature could be easily felt.

The sketch of the experiment: Experiment

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  • $\begingroup$ You need to explain your experiment in more detail: what steps are you taking, what materials are you using, what are you expecting in terms of noticeable results? I suspect the process is isothermal though $\endgroup$
    – bleuofblue
    Mar 13, 2022 at 23:15
  • $\begingroup$ What's the mass of the gas inside? What's the mass and material of the syringe? What's the relative heat capacity of the gas and the syringe? $\endgroup$
    – BowlOfRed
    Mar 13, 2022 at 23:20
  • $\begingroup$ Is your thermometer coupled to the gas inside the syringe, with little thermal contact to the much larger heat capacity of the syringe? If so the ideal gas law will work just fine. $\endgroup$
    – rfl
    Mar 14, 2022 at 13:23

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In calculating your expectation, you are neglecting the heat capacity of your experiment. Once you take that into account, you will find that your gas will get cold, but there isn't enough energy to cool the syringe by any significant amount; Also, you are neglecting time, which has the effect that the syringe and gas is being heated by the environment while your cooler gas is supposed to cool the syringe and your finger. Taken together, I would not expect anything.

To make your experiment work, use a thermometer with a small heat capacitance, directly inside the syringe, to measure the temperature of the gas. That will work just fine. Commercial suppliers do offer similar experiments to demonstrate the ideal gas law, see e.g. here or a simple search on youtube.

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  • $\begingroup$ In fact, the estimated heat that the air needs in order to warm to 20°C is around $5\cdot 10^{-4} \rm\, J$. $\endgroup$
    – User123
    Mar 14, 2022 at 15:51
  • $\begingroup$ The change is still adiabatic (if we pull it quickly), isn't it? $\endgroup$
    – User123
    Mar 16, 2022 at 16:45
  • $\begingroup$ Sure, but the ideal gas law will work just fine too $\endgroup$
    – rfl
    Mar 17, 2022 at 5:56

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