# PV Diagrams- Thermodynamics

• racky tak

## Homework Statement

A cylinder with a piston contains 0.250 mol of oxygen at 2.40  105 Pa and 355 K. The oxygen may be treated as an ideal gas. The gas first expands isobarically to twice its original volume. It is then compressed isothermally to its original volume, and then it is cooled isochorically to its original pressure.(a) Show the series of processes on a pV – diagram. (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. (e) Find the absolute value of the total heat flow into or out of the gas for this sequence of processes, and state the direction of heat flow.

I just don't know where to go with part e- i think I'm confused on that part, oever, the other sections a through d i think i got here is my attempt at a solution.

## The Attempt at a Solution

a) The pV-diagram I figured out this part.
Temperature Ta = 355K,
Pa = Pb = 2.40 x 105Pa,
andnumber of moles, n = 0.250mol.
∴Volumeat state a,
= 3.074 x 10-3m3.
(b)
Volume in state b ,Vb = 2Va
= 6.149 x 10-3m3.
Let Tb is the temperature at point b.
Since Pa = Pb and Vb = 2Va, then Tb = 2Ta = 710K.

(c) The maximum pressure Pc is at point c.
At point c, the volume is Va, and the temperature is Tb.
∴Pressurein state c,
= 4.80 x 105Pa.
(d)
Total work done by the piston on the gas during the series of processes,
Wab = Pa(Vb - Va)
= (2.40 x 105Pa)(3.074 x 10-3m3)
= 737.867J.
=
= (0.250mol)(8.314J/mol K)(710K)(-ln2)
= -1022.9J.
The total work done is W = Wab + Wbc = -285J.

Your answer for the work has the wrong sign. You calculated the work done by the gas on the piston, but the problem asked you for the work done on the gas by the piston.

For part e, you need to use the first law. You already calculated the work for each process. If you can figure out the change in internal energy of the gas for each process, you can find the heat transferred.