Equations that describe ideal gas processes

[physea]

Hello!
Is there a table to show the equations that describe ideal gas processes?
For example, I know for isothermic, it's P1V1=P2V2, what about the others?

Also, how are these derived? Is it from Q-W=dU? or PV=nRT?
Any help?
thanks!

 

[DrClaude]

Is there a table to show the equations that describe ideal gas processes?

Check out:
https://en.wikibooks.org/wiki/Physical_Chemistry/Thermodynamic_Processes_for_an_Ideal_Gas
https://chem.libretexts.org/Core/Ph...rmodynamics/Ideal_Systems/Ideal_Gas_Processes

For example, I know for isothermic, it's P1V1=P2V2, what about the others?

Also, how are these derived? Is it from Q-W=dU? or PV=nRT?

It depends. Sometimes one, sometimes the other, sometimes both. For instance, can you see how you get the isothermal equation you stated?

 

[ZapperZ]

Hello!
Is there a table to show the equations that describe ideal gas processes?
For example, I know for isothermic, it's P1V1=P2V2, what about the others?

Also, how are these derived? Is it from Q-W=dU? or PV=nRT?
Any help?
thanks!

This is a bit puzzling.

The ideal gas law equation is

pV = nRT

or

pV = NkT

Those two are the same thing and can be derived from one another.

Everything else, depending on what is kept constant, are written using that equation. For example, for isothermic reaction that you described, T is a constant, so the equation can be written as

pV = nRT = constant

meaning that the produce of p and V are constant throughout the change, i.e. p₁V₁ = p₂V₂.

For isobaric process, you have constant p, so rewriting it, you get

V/T = nR/p = constant.

This time, V and T are constants, so V₁/T₁ = V₂/T₂.

And so on. These are NOT separate equations because they are all derived from the "mother" equation, which is the ideal gas law. Asking for a table of such equations means that you do not understand that they are all from the same equation, not to mention, it may mean that you are memorizing many different forms of the same equation unnecessarily.

Zz.

 

[Chestermiller]

This is a bit puzzling.

The ideal gas law equation is

pV = nRT

or

pV = NkT

Those two are the same thing and can be derived from one another.

Everything else, depending on what is kept constant, are written using that equation. For example, for isothermic reaction that you described, T is a constant, so the equation can be written as

pV = nRT = constant

meaning that the produce of p and V are constant throughout the change, i.e. p₁V₁ = p₂V₂.

For isobaric process, you have constant p, so rewriting it, you get

V/T = nR/p = constant.

This time, V and T are constants, so V₁/T₁ = V₂/T₂.

And so on. These are NOT separate equations because they are all derived from the "mother" equation, which is the ideal gas law. Asking for a table of such equations means that you do not understand that they are all from the same equation, not to mention, it may mean that you are memorizing many different forms of the same equation unnecessarily.

Zz.

In addition to the ideal gas law, another equation that characterizes ideal gas behavior is dU=mCvdT

 

[physea]

Check out:
https://en.wikibooks.org/wiki/Physical_Chemistry/Thermodynamic_Processes_for_an_Ideal_Gas
https://chem.libretexts.org/Core/Ph...rmodynamics/Ideal_Systems/Ideal_Gas_ProcessesIt depends. Sometimes one, sometimes the other, sometimes both. For instance, can you see how you get the isothermal equation you stated?

Thanks the first link is spot on.
But it doesn't explain what Cv and Cp is, any hint?

 

[ZapperZ]

Thanks the first link is spot on.
But it doesn't explain what Cv and Cp is, any hint?

So you are being taught ideal gas law, but you haven't gone over the concept of heat capacity?

This is very odd. What school is this?

Zz.

 

[Chestermiller]

Thanks the first link is spot on.
But it doesn't explain what Cv and Cp is, any hint?

$$C_v\equiv \left(\frac{\partial U}{\partial T}\right)_V$$For an ideal gas, ##C_p=C_v+R##, where, in these equations, all the quantities are per mole.