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# 8.5: The Clément-Desormes Experiment

• • Jeremy Tatum
• Emeritus Professor (Physics & Astronomy) at University of Victoria

This is a simple, quick and effective experiment often seen in teaching laboratories for measuring γ for air, or, with some extra effort, any other gas.

Sometimes this experiment is referred to as the experiment of Clément and Desormes, and sometimes as the experiment of Clément-Desormes. Apparently Charles-Bernard Desormes was the uncle of Nicolas Clément, and they both worked on the experiment. Nicolas Desormes later legally changed his name to Nicolas Clément-Desormes. Thus you can refer either to the experiment of Clément and Desormes or to the experiment of Clément-Desormes!

A bottle of air starts at P1, T1. Pl is a little greater than atmospheric pressure P0. T1 is the ambient room temperature. The bottle is provided with some device for measuring pressure (for example, a manometer). We'll see that there is no need to measure temperatures. The stopcock is quickly opened and immediately closed. The pressure at that moment is just atmospheric pressure, which I'll call P0, and the temperature is T2, which is a little cooler than the original room temperature T1. The bottle of gas is now allowed slowly to warm up isochorically to its original temperature Tl, by which time the new pressure P2 is greater than atmospheric pressure P0 but not as large as the original pressure P1. You should sketch these two stages on a PV diagram.

$P_{1}^{-(\gamma-1)} T_{1}^{\gamma}=P_{0}^{-(\gamma-1)} T_{2}^{\gamma}.$

For the isochoric process,

$P_{0} / T_{2}=P_{2} / T_{1}.$

I'll leave you to do the algebra and eliminate T2/T1 from these equations and hence show that

$\gamma=\frac{\ln \left(P_{1} / P_{0}\right)}{\ln \left(P_{1} / P_{2}\right)}.$

In the above analysis, we assumed that the gas was ideal and the expansion was adiabatic and reversible. The gas is nearly ideal if it is a long way above its critical temperature and there are no enormous ranges of P and T. The expansion is adiabatic if P2 is measured immediately after the stopcock is opened and closed, so that there is no time for heat to enter or leave the system. It is reversible only if P1P0 << P0. If you want to do the experiment yourself right now without getting up from your comfortable seat, have a look at http://www.univ-lemans.fr/enseignements/physique/02/thermo/clement.html