The experimental setup for the main measurements is as follows. The syringe containing a trapped air volume $V$ is connected to the tube. The other end of the tube is open to the atmosphere. A water droplet inside a tube acts as a frictionless movable piston, so the pressure of the trapped air remains equal to the atmospheric pressure. Assume that the ambient temperature $T_0$ is constant at $20^\circ\mathrm{C}$.
When the temperature of the air inside syringe changes, the air expands/or compresse, causing the droplet to move. The position $x$ of the droplet's edge is related to the air temperature $T=T_0+\Delta$ inside the syringe by the following equation:
\[x = x_0 + \frac{V}{S} \frac{\frac{\Delta T}{T_0+273^\circ\mathrm{C}}}{1 + \frac{\Delta T}{T_0+273^\circ\mathrm{C}}},\]where $x_0$ is the initial position of droplet's edge when the syringe air temperature is equal to the ambient temperature (i.e. $\Delta T =0$).
Carefullу assemble the setup with the syringe volume set to $V=10.0~\mathrm{ml}$. Then, hold the syringe barrel in your hand and observer the droplet starting to move.
Put the syringe on the table and observe the droplet returning to its initial position. Wait for $10~\mathrm{min}$ to allow the syringe and the air inside it to cool down to ambient temperature.
For convenience, you may draw out and push in air between trials.
During the measurements in Part A you likely noticed that after heating the syringe to temperature $T_\mathrm{h}$ and placing it on the table, the droplet gradually returns to its initial position. This occur due to to heat losses from the syringe to the environment. The dependence of the air temperature $T$ inside the syringe on time $t$ can be described by the following equation:
\[T = T_0 + (T_\mathrm{h}- T_0) \cdot e^{-t/\tau},\]where $\tau$ is the characteristic thermal relaxation time of the process.
Place the syringe on the table and start the stopwatch simultaneously. Record the dependence of $x$ on time $t$. Perform 12 measurements.