Calculating work in a one-step expansion/compression

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The discussion centers on solving a thermodynamics problem involving an ideal gas undergoing an irreversible process at constant temperature. The key points include the use of the ideal gas law (PV=nRT) to determine the initial volume of gas, followed by applying Boyle's Law (P1V1=P2V2) to find the new volume after pressure changes. The work done during the process is calculated by multiplying the new pressure by the change in volume (ΔV) between the initial and final states. If only the net transition work is needed, the intermediate step can be disregarded, simplifying the calculations.
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Hello. I'm having problems with one thermodynamics. I've used several equations but I'm still unable to get the right answer. A push in the right direction would be helpful. Thanks.


Consider a process involving 1 mole of an ideal gas that takes place by the following pathway, at a constant temperature of 25oC:
P1 = 3 atm → P2 = 0.75 atm → P3 = 3 atm
Both steps occur irreversibly.

work=?
 
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W=P[delta]V

Boyle's Law: P1V1=P2V2

PV=nRTSo, use the ideal gas equation (PV=nRT) to solve for the initial volume of gas present. Then you can use Boyle's law to calculate the new volume after the change has occurred (the new volume is V2, the initial pressure is P1, etc) you can then multiply the new pressure by the CHANGE in volume (ie, the difference between V1 and V2) to get the work. Repeat process for the next step of the transfer. If you only need to calulate work for the net transition, completely ignore the middle step.
 

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