Thermodynamics, Isothermal Question

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SUMMARY

The discussion centers on a thermodynamics problem involving 10 moles of an ideal gas transitioning from a state of P1 = 10 atm and T1 = 300K to P = 1 atm at T = 300K. The initial calculation of work done during the cycle was incorrectly derived as 57.4 kJ, while the correct value is 123.4 kJ. The error arose from misunderstanding the nature of the process, which is not isothermal due to the straight-line path on the P-V diagram, indicating a change in temperature rather than a constant temperature throughout the process.

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kalbuskj31
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Homework Statement



10 moles of an ideal gas, in the initial state P1 = 10 atm, T1 = 300K are taken around the following cycle.

a) A reversible change of state along a straight line path on the P-V diagram to the state P = 1 atm T = 300K. How much work is done during the cycle?

Homework Equations



Isothermal, ΔU = 0 so w = p dV

The Attempt at a Solution



w = p dV and p = nRT/V so w = nRT (dV/V)

w = nRT ln(Vf/Vi) = nRT ln(Pi/Pf)

w = [(10 moles)* (8.3144 J/ K *mole) * (300K)] ln(10atm/1atm)

w = 57.4 kJ but the correct answer is 123.4kJ. Suggestions??
 
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The process is not isothermal. You are not taking into account that the graph is a straight line.

You are finding the area under the isothermal curve between the beginning and ending points (PV = constant).

AM
 
Andrew Mason said:
The process is not isothermal. You are not taking into account that the graph is a straight line.

You are finding the area under the isothermal curve between the beginning and ending points (PV = constant).

AM

Thanks. Can you please explain why this process isn't considered isothermal?
 
kalbuskj31 said:
Thanks. Can you please explain why this process isn't considered isothermal?

An isotherm has the same temperature during the whole process, not just at the start and end points. It will look like an exponential curve on the PV diagram. Adiabats will be "steeper" because they cross the isotherms.

Since it's a straight line, did you try a graphical integration?
 
Thank you for the help. the graphical interpretation helped give me the correct answer. I've been out of school for 3 years, so I'm brushing up on everything.
 

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