Chem Paster 2.1

Notebook 2.1: Work in Reversible Isothermal Expansions

This short exercise gives students more practice using Maxima’s integration and comma operators.

Download and install the Euler Math Toolbox . Cut and paste the code below into a plain text file. Save the file with an .en file extension. Double-click the file. It should open up in the Toolbox.

All of the notebooks in this series are specifically keyed to Atkins’ Physical Chemistry , 8th edition. Italics mark the items students had to fill in themselves.

--------------------------------------------------------snip here---------------------------------------------------- Notebook 2.1: Work in Reversible Isothermal Expansions % % In reversible expansions or compressions, the external pressure constantly changes so that % it remains exactly equal to the pressure of the gas. In this special case, we can substitute % the pressure calculated from the gas's equation of state for the external pressure when calculating work. % For example, the work done to compress n moles of an ideal gas from V1 to V2 under reversible % conditions at temperature T is % >: assume(V1>0, V2>0, V1>V2, V>0) [V1 > 0, V2 > 0, V1 > V2, V > 0] >: work_ideal: -integrate(n*R*T/V,V,V1,V2) n R T (log(V1) - log(V2)) % If the "assume" had been omitted, Maxima would have asked a series of questions about % the signs of the volumes during the integration. % % If we want to calculate the work for specific temperatures and volumes, we can use Maxima's % comma operator. For example, >: work_ideal, n=1, R=8.314, T=298, V1=1, V2=0.5, numer 1717.322046434265 % % Integrating -n*R*T/V with respect to V from V1 to V2 at constant T gives -n*R*T*ln(V2/V1), so we could % also have calculated the work as -n*R*T*log(V2/V1). % --> Notice that the Maxima function for natural logarithms is log(), NOT ln()!) % --> The final ",numer" tells Maxima that we want a number as an answer. Maxima will sometimes % just display logs of whole numbers without calculating them in a final result if we don't include this. % --------------------------------------------------------------------------------------------------------- % In the space below, create an expression called work_vdw that calculates the work for a reversible isothermal % expansion of a van der Waals gas as it expands from volume V1 to volume V2 at temperature T.

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