# Why doesn't temperature decrease with an increase of volume in the syringe?

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:

• 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 Mar 13, 2022 at 23:15
• 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? Mar 13, 2022 at 23:20
• 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.
– rfl
Mar 14, 2022 at 13:23

• In fact, the estimated heat that the air needs in order to warm to 20°C is around $5\cdot 10^{-4} \rm\, J$. Mar 14, 2022 at 15:51