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Handmade warmth

A1  0.80 Determine the cross section area $S$ of the tube.

1 Correct method is described 0.60
2 \[S \in [0.058,0.088]~\mathrm{cm}^2\] 0.20
A2  0.20 Choose the direction of the droplet's motion.

1 Towards open end 0.20
A3  2.50 For 5 different volumes $V$ perform the experiment and record the values of $x_0$ and $x$. Ensure the system reaches equilibrium before taking measurements!

For convenience, you may draw out and push in air between trials.

1 Measurements of $x$ and $x_0$ 5 × 0.40
2 \[V_\mathrm{max} - V_\mathrm{min} \geq 6~\mathrm{ml}\] 0.50
A4  1.00 Plot the graph of $x-x_0$ vs. $V$.

1 Graph is plotted 1.00
2 Labels of axes are missing -0.20
3 Poor scale -0.20
4 Poor ticks -0.20
5 There is no fitting line -0.20
A5  1.00 Determine the temperature $T_\mathrm{h}$ of your hand. Calculate the ratio $(T_\mathrm{h} - T_0)/(T_0 + 273^\circ\mathrm{C})$?

1 Explicetly stated that $\mathrm{slope}$ is equal to
\[\frac{1}{S} \cdot \dfrac{\frac{\Delta T}{T_0 + 273^\circ\text{C}}}{1+\frac{\Delta T}{T_0 + 273^\circ\text{C}}}\]
0.20
2 $\mathrm{slope} \in [0.3,0.8]~\mathrm{cm}/\mathrm{ml}$ 0.20
3 \[T_\mathrm{h} \in [27,36]^\circ\text{C}\] 0.40
4 \[\frac{\Delta T}{T_0 + 273^\circ\text{C}}\in[0.024,0.054]\] 0.20
B1  1.80 Assemble setup with $V=10~\mathrm{ml}$. Record the value of $x_0$. Heat the syringe to temperature $T_\mathrm{h}$.

Place the syringe on the table and start the stopwatch simultaneously. Record the dependence of $x$ on time $t$. Perform 12 measurements.

1 Value of $x_0$ is specified 0.10
2 Measurements of $x$ on $t$ 12 × 0.10
3 Total duration is greater than $5~\mathrm{min}$ 0.50
B2  2.50 Choose the coordinates in which the dependence of $x$ on $t$ becomes linear and plot the corresponding graph.

1 \[\ln (x-x_0) = C - \frac{t}{\tau}\] 1.00
2 Linearized graph is plotted 1.00
3 Axes labels are missing -0.20
4 Poor scale -0.20
5 Poor ticks -0.20
6 There is no fitting line -0.20
7 $\mathrm{slope}\in [-6.0,-4.0]\cdot 10^{-3} ~\mathrm{s}^{-1}$ 0.50
B3  0.20 Determine the value of $\tau$.

1 \[\tau \in [150,250]~\mathrm{s}\] 0.20