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## Homework Statement

A cylindrical container is sealed with a movable piston and contains [itex]0.200[/itex] mol of oxygen. The initial pressure is [itex]2.5 × 10^5[/itex] Pa and the initial temperature is [itex]77◦C[/itex]. The value of the ideal gas constant is [itex]R = 8.315[/itex]J/mol · K. The oxygen, which can be approximated as an ideal gas, first undergoes an isobaric expansion to twice its original volume. It is then compressed isothermally back to its original volume. Finally, it is cooled isochorically to its original pressure.

(a) Give a definition of isobaric, isothermal, and isochoric transformations. Show the series of processes on a p-V diagram. Label your diagram clearly.

(b) Compute the temperature during the isothermal compression.

(c) Compute the maximum pressure.

(d) Compute the total work done by the piston on the gas during the series of processes.

(e) Compute the oxygen’s internal energy change during the initial isobaric expansion. Use CP = 29.17 J/mol · K. (f) Compute the oxygen’s internal energy change during the isothermal compression.

## Homework Equations

## The Attempt at a Solution

I have done parts a, b and c without a problem, but I have a small question regarding part d.

The work done by the isobaric process is [itex]W = P(\Delta V)[/itex], and the work done by the isothermal process is given by [itex]W = nRT ln(\frac{V_{f}}{V_{i}})[/itex].

The work done by the isothermal process seems to count the work done during the Isobaric process twice. Is this correct, or would the work done by the Isothermal process in this case be [itex]W = nRT ln(\frac{V_{f}}{V_{i}}) - P(\Delta V)[/itex]?

Thanks!