Isothermal exapansion, work done

[Saxby]

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 :)

 

[sankalpmittal]

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.

 

[Saxby]

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.

 

[sankalpmittal]

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.