Isothermal exapansion, work done

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SUMMARY

The discussion focuses on deriving the expression for work done during the isothermal expansion of one mole of an ideal gas from an initial volume V1 to a final volume V2 at a constant temperature T. The relevant equations include the ideal gas law (PV = nRT) and the work done formula (W = V2∫V1Pdv). The correct expression for work done in this scenario is W = RT * ln(V2/V1), derived by substituting pressure in the work formula and performing integration. The importance of considering whether the process is reversible or irreversible is also highlighted.

PREREQUISITES
  • Understanding of the ideal gas law (PV = nRT)
  • Knowledge of calculus, specifically integration techniques
  • Familiarity with thermodynamic processes, particularly isothermal expansion
  • Concept of reversible vs. irreversible processes in thermodynamics
NEXT STEPS
  • Study the derivation of work done in isothermal processes in detail
  • Learn about the differences between reversible and irreversible thermodynamic processes
  • Explore applications of the ideal gas law in real-world scenarios
  • Investigate the implications of isothermal expansion on system efficiency
USEFUL FOR

Students studying thermodynamics, physics enthusiasts, and anyone looking to understand the principles of gas expansion and work done in isothermal conditions.

Saxby
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Homework Statement


Derive an expression for the amount of work done when one mole of an ideal gas expands isothermally at a temperature T from an initial volume V1 to a final volume V2.


Homework Equations


PV = nRT
W = V2∫V1Pdv

The Attempt at a Solution


I'm not really sure how to go about this, I know if it's isothermal the temperature doesn't change so Volume would be inversely proportional to Pressure. But other than that i don't know what to do, to be honest I'm not really exactly what they want me to write. Any help would be much appreciated :)
 
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Saxby said:

Homework Statement


Derive an expression for the amount of work done when one mole of an ideal gas expands isothermally at a temperature T from an initial volume V1 to a final volume V2.


Homework Equations


PV = nRT
W = V2∫V1Pdv

The Attempt at a Solution


I'm not really sure how to go about this, I know if it's isothermal the temperature doesn't change so Volume would be inversely proportional to Pressure. But other than that i don't know what to do, to be honest I'm not really exactly what they want me to write. Any help would be much appreciated :)

The question seems to be incomplete. It is isothermal expansion , fine. But its isothermal reversible or isothermal irreversible process , its just not mentioned.

I ask you a question : Do you want to calculate maximum work done by the gas , or not in an isothermal process. If former , consider the process reversible , else irreversible.

Oh , they do not concern you about external pressure. Consider your process reversible then.

Hint :

W = V2∫V1Pdv ...(i)

PV=nRT => P=nRT/V

Now replace this value of P in (i) and carry on your integration.
 
Thanks for the Hint that's makes sense, my final answer (upon using that hint) would be W = RT * Ln(V). I think that's the answer but i'll try and confirm it with my lecturer tommorow if i can. Thanks for your help.
 
Saxby said:
Thanks for the Hint that's makes sense, my final answer (upon using that hint) would be W = RT * Ln(V). I think that's the answer but i'll try and confirm it with my lecturer tommorow if i can. Thanks for your help.

No you should get W=RT*ln(V2/V1)

See your integral again. Be careful while doing integration.
 

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