02 Fire-Pump

Aim¶

To show that fast compression is accompanied by a considerable raise in temperature.

Subjects¶

• 4B70 (Adiabatic Processes)

Diagram¶

Equipment¶

• Closed tube, fitted with plunger.

• Pyroxyl wire.

Presentation¶

Small pieces of pyroxyl are put in the tube. The plunger is fitted into the tube and then pushed down rapidly. The pyroxyl lights and burns with a flash (see DiagramB). This points out to a steep increase in temperature.

Explanation¶

In general the process of the gas is polytropic, so: $p V^{n}=$ constant. In this demonstration the air in the closed tube is compressed rapidly, so during this action there is almost no heat exchanged with the surroundings. Such a process is performed adiabatically, and $n=\gamma$, giving $p V^{\gamma}=$ constant. Rewriting this in terms of temperature gives: $T V^{\gamma-1}=$ constant and so: $T_{2}=\left(\frac{V_{1}}{V_{2}}\right)^{\gamma-1} T_{1}$.

When the compression ratio $\left(\frac{V_{1}}{V_{2}}\right)$ is around 6 and using air $(\gamma=1.4)$ we have: $T_{2}=6^{0.4}$.

$T_{1}=2 T_{1}$. So starting at room temperature ( $T_{1}=300 \mathrm{~K}$ ), the air should heat up to around $600 \mathrm{~K}\left(327^{\circ} \mathrm{C}\right)!$

Remarks¶

• Hold the tube firmly, so that when you press the plunger downwards forcefully the tube doesn’t topple and break. We prevent toppling by standing on the foot of the construction.

• When the flash occurs you can feel also the rise in pressure

• We use pyroxyl wire, but you can also use small pieces of paper and/or the scrapings of a match. But do not use too much; more material means a higher heat capacity and as a consequence a lower temperature-rise of that material.

Sources¶

• Mansfield, M and O’Sullivan, C., Understanding physics, pag. 279-281.

• Meiners,H., Physics demonstration experiments, part 2, pag. 800.

• Wolfson, R., Essential University Physics, pag. 297-299.