Calculating Work Done by an Ideal Gas in a Three-Step Transformation

AI Thread Summary
The discussion revolves around calculating the work done by a monatomic ideal gas during a three-step transformation involving heating, expansion, and cooling. The user seeks assistance in determining the work done during the second step of the process, where the gas expands at constant temperature until the pressure returns to its initial value. The key challenge is finding pressure as a function of volume to perform the necessary integral for the calculation. The user eventually finds the answer and expresses gratitude to the forum for the help received. The conversation highlights the application of the ideal gas law in thermodynamic processes.
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A monatomic ideal gas has pressure p_1 and temperature T_1. It is contained in a cylinder of volume V_1 with a movable piston, so that it can do work on the outside world.

Consider the following three-step transformation of the gas:

1. The gas is heated at constant volume until the pressure reaches A p_1 (where A >1).
2. The gas is then expanded at constant temperature until the pressure returns to p_1.
3. The gas is then cooled at constant pressure until the volume has returned to V_1.

It may be helpful to sketch this process on the pV plane.

How much work W_2 is done by the gas during step 2?
Express the work done in terms of p_1, V_1, and A.

I know I have to find the integral, but I can't work out how to find pressure as a function of volume.

Please help.

Thank you
 
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