Calculate Work (w) for Isothermal Gas Expansion/Compression

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SUMMARY

The discussion focuses on calculating the work (w) done during isothermal expansion or compression of an ideal gas, specifically using the formula w = -nRT ln(V2/V1). The participants clarify that for isothermal processes, nRT remains constant and can be substituted with PV from the ideal gas law (PV = nRT). The initial and final pressures and volumes can be used interchangeably in the calculations, as long as they correspond to the same state. The key takeaway is that nRT does not change during the process, and thus can be evaluated at any state along the isothermal path.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV = nRT)
  • Knowledge of isothermal processes in thermodynamics
  • Familiarity with natural logarithms and their application in physics
  • Basic algebra for manipulating equations
NEXT STEPS
  • Learn about the derivation and application of the work formula for isothermal processes
  • Study the implications of the Ideal Gas Law in different thermodynamic processes
  • Explore the concept of reversible vs. irreversible processes in thermodynamics
  • Investigate the relationship between pressure, volume, and temperature in real gases
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Students and professionals in chemistry and physics, particularly those studying thermodynamics, ideal gas behavior, and isothermal processes.

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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Welcome to PF!
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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