Work Done in an Isothermal Process

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A piston sits atop a cylinder filled with 0.04 moles of an ideal gas. The cylinder is surrounded by a constant temperature bath. A digital temperature probe, which reads the gas temperature in °C, is attached to the cylinder. A digital pressure sensor, which reads the pressure in kPa, is also attached. Play the animation to push the piston down into the cylinder, and see how the volume and pressure change on the accompanying PV plot and in the data table below. The table also displays the total work done by the gas since the process began. What can you conclude?

Hints:

  1. What is the initial volume, Vi, of the gas at the beginning of the process?
  2. Play the animation and pause it several times to verify that PV = constant.
  3. At the end of the animation, what is the final volume, Vf?
  4. What is the (constant) gas temperature, T,  in Kelvins?
  5. How should the total work done in this process depend on T, Vf  and Vi?
  6. Why is the sign of the work in this particular process negative?

Reference

See Serway and Beichner, Physics For Scientists and Engineers 5th Edition, Section 20.6

Illustration written by Steve Mellema and Chuck Niederriter