Thermodynamic Processes: Ideal Gas Expansion and Compression

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The discussion revolves around a thermodynamics homework problem involving the expansion and compression of an ideal gas. The gas, oxygen, undergoes an isobaric expansion to double its volume, followed by isothermal compression back to its original volume, and finally an isochoric cooling to its initial pressure. Participants emphasize using the ideal gas law (PV=nRT) to calculate the temperature during isothermal compression and the work done by the piston. The maximum pressure is noted to be double the initial pressure due to the isobaric process. Ultimately, the original poster successfully resolves the problem with the provided guidance.
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Homework Statement



A cylinder with a piston contains 0.250 moles of oxygen at 2.40 * 10^5 Pa and 355K. The oxygen may be treated as an ideal gas. The gas first expands isobarically to twice its original volume. It is then compressed isothermally back to its original volume, and finally it is cooled isochorically to its original pressure

Compute the temperature during the isothermal compression.
Compute the maximum pressure.
Compute the total work done by the piston on the gas during the series of processes.

Homework Equations





The Attempt at a Solution



For the first question Compute the temperature during the isothermal compression, I really have no idea how to start. I've been searching through my lecture notes and textbook for an hour and I just can not figure out a strategy to calculate it.

I've calculated the maximum pressure because it's simply double the initial, and if I could just solve for the T in part 1 I could calculate the work done. Very frustrated please help!
 
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The oxygen may be treated as an ideal gas

Use the ideal gas equation

To find the work you need only information about the volume and pressure
 
If you remember that isobaric means the pressure remains constant you can find the temperature during the expansion. Then during the compression, the problem says the temperature does not change because it is an isothermic compression.

Find the temperature from the ideal gas equation: \ PV=nRT

This also may help: \ P_1V_1 / P_2V_2 = T_1 / T_2 (if the pressure is the same, what does this simplify to?)
 
Thanks guys I have solved the question!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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