Determining Q for Isobaric Processes: Cp or Cv?

[songsteel]

Just wanted to ask why is it that for isobaric processes, when we wanted to find Q, sometimes we use Q = nCpΔT and sometimes we use Q = nCvΔT + p(Vf - Vi)?

How do we determine which should be used and when?

 

[Tanya Sharma]

Just wanted to ask why is it that for isobaric processes, when we wanted to find Q, sometimes we use Q = nCpΔT and sometimes we use Q = nCvΔT + p(Vf - Vi)?

How do we determine which should be used and when?

They are not different things .Both of the above expressions are correct and can be used simultaneously , or separately depending on the situation.

For an isobaric process ΔQ = nC_PΔT.

From First law of Thermodynamics ΔQ = ΔU+ΔW .

Now ΔU=nC_VΔT applies to all kinds of processes involving an ideal gas.

So ,putting values of ΔQ and ΔU ,we have nC_PΔT = nC_VΔT + pΔVTo elaborate it further-

Case 1) What is the heat required to raise the temperature of 'n' moles of an ideal monoatomic gas by 'ΔT' .

You can simply use Q = nC_PΔT

Case 2) How much heat is supplied to 'n' moles of an ideal monoatomic gas in a chamber fitted with a light piston , when the temperature changes by 'ΔT' and volume changes by ΔV ? Consider the process to be isobaric

Here ,use ΔQ = nC_VΔT + pΔV

Case 3) What is the change in the volume of 'n' moles of an ideal monoatomic gas in a chamber fitted with a light piston , when the temperature changes by 'ΔT' ? Consider the process to be isobaric .

Now use nC_PΔT = nC_VΔT + pΔV

Edit:Removed the word - "insulated" and removed a typo

 

[Chestermiller]

They are not different things .Both of the above expressions are correct and can be used simultaneously , or separately depending on the situation.

For an isobaric process ΔQ = nC_PΔT.

From First law of Thermodynamics ΔQ = ΔU+ΔW .

Now ΔU=nC_VΔT applies to all kinds of processes involving an ideal gas.

So ,putting values of ΔQ and ΔU ,we have nC_PΔT = nC_VΔT + pΔV


To elaborate it further-

Case 1) What is the heat required to raise the temperature of 'n' moles of an ideal monoatomic gas by 'ΔT' .

You can simply use Q = nC_PΔT

Case 2) How much heat is supplied to 'n' moles of an ideal monoatomic gas in an insulated chamber fitted with a light piston , when the temperature changes by 'ΔT' and volume changes by ΔU ? Consider the process to be isobaric

Here ,use ΔQ = nC_VΔT + pΔV

Case 3) What is the change in the volume of 'n' moles of an ideal monoatomic gas in an insulated chamber fitted with a light piston , when the temperature changes by 'ΔT' ? Consider the process to be isobaric .

Now use nC_PΔT = nC_VΔT + pΔV

Hi Tanya. You need to "lose" the word insulated from cases 2 and 3. If Q is not equal to zero, the chamber is not insulated. In all three cases, you need to lose the word monoatomic, and in case 1 you need to add the words at "at constant volume". Also, in item 2 there is a typo: replace ΔU with ΔV.

Chet

 

[Tanya Sharma]

Hi Chet...

Hi Tanya. You need to "lose" the word insulated from cases 2 and 3. If Q is not equal to zero, the chamber is not insulated.

Yes you are right .I have edited my post.

In all three cases, you need to lose the word monoatomic,

Why? These are just examples i have taken using monoatomic ideal gas.

and in case 1 you need to add the words at "at constant volume".

Why ? The heat supplied at constant pressure is nC_PΔT

 

[Chestermiller]

Hi Chet...

Why? These are just examples i have taken using monoatomic ideal gas.

It might give the impression that the relationship applies only to a monoatomic ideal gas.

Why ? The heat supplied at constant pressure is nC_PΔT

Oh, sorry. I misread the C_p as C_v. I think it would be worthwhile adding the words "at constant pressure" to Case 1.

Chet

 

[Tanya Sharma]

It might give the impression that the relationship applies only to a monoatomic ideal gas.

Well..these are just random questions/cases I formed .But...you may be correct.

Oh, sorry. I misread the C_p as C_v. I think it would be worthwhile adding the words "at constant pressure" to Case 1.

Chet

Right.

Thanks for your valuable suggestions .I very much like reading your posts .They are full of insight.