Calculate Work (w) for Isothermal Gas Expansion/Compression

AI Thread Summary
To calculate the work done (w) during isothermal gas expansion or compression, the equation w = -nRT ln(V2/V1) is applicable, where nRT remains constant throughout the process. The ideal gas law (PV = nRT) can be used to substitute for nRT, as it equals PV at any state. The values for pressure (P) and volume (V) can be taken from either the initial or final states, as they will yield the same result due to the relationship P1V1 = P2V2. It is important to note that nRT does not correspond to a change in pressure and volume, as it remains constant during the isothermal process. Understanding these relationships clarifies how to approach the problem effectively.
IoFawkes
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Homework Statement


Calculate Work(w) when 6.5L of an ideal gas at an initial pressure of 34.3atm is expanded or compressed isothermally to a final volume of 34.3L reversibly. Answer in J

Homework Equations


PV=nRT
P1V1=P2V2
w=-nRT In(V2/V1)

The Attempt at a Solution


Using w=-nRT In(V2/V1)
I'm not given mols or T, I know T=constant, since it's isothermal
Can I use PV=nRT and substitute (PV) in for (nRT) in the equation: w=-nRT In(V2/V1) ?
If so, what should I use for values of P and V? Final/Initial/delta?

Io

PS: This may be in the wrong place, the boundary seems unclear in Chem/Phys or Phys/Chem studies.
 
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IoFawkes said:
Can I use PV=nRT and substitute (PV) in for (nRT) in the equation: w=-nRT In(V2/V1) ?
Yes
If so, what should I use for values of P and V? Final/Initial/delta?
How does PV in the initial state compare to PV in the final state?
 
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TSny said:
How does PV in the initial state compare to PV in the final state?
P1V1=P2V2 so it doesn't matter which I use as long as P and V are both initial values, or final values. Correct?
EDIT: Except it's asking for work done, so would it be the Change in Pressure and Volume?
Io
 
Last edited:
IoFawkes said:
P1V1=P2V2 so it doesn't matter which I use as long as P and V are both initial values, or final values. Correct?
Yes
EDIT: Except it's asking for work done, so would it be the Change in Pressure and Volume?
nRT is a constant for an isothermal process. At any point along the process, nRT has the same value. The ideal gas law tells us that for any state, nRT = PV. So, nRT for the isothermal process equals PV evaluated for any state along the isothermal process.

nRT would not correspond to a change in PV.
 
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TSny said:
nRT is a constant for an isothermal process. At any point along the process, nRT has the same value. The ideal gas law tells us that for any state, nRT = PV. So, nRT for the isothermal process equals PV evaluated for any state along the isothermal process.

nRT would not correspond to a change in PV.

Ah, that makes sense, thanks! How wonderful a change in perspective.

Io
 
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