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Q for Isobaric Processes

  • Thread starter songsteel
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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?
 

Answers and Replies

  • #2
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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 = nCPΔT.

From First law of Thermodynamics ΔQ = ΔU+ΔW .

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

So ,putting values of ΔQ and ΔU ,we have nCPΔT = nCVΔT + 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 = nCPΔT

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 = nCVΔT + 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 nCPΔT = nCVΔT + pΔV

Edit:Removed the word - "insulated" and removed a typo
 
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  • #3
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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 = nCPΔT.

From First law of Thermodynamics ΔQ = ΔU+ΔW .

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

So ,putting values of ΔQ and ΔU ,we have nCPΔT = nCVΔT + 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 = nCPΔT

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 = nCVΔT + 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 nCPΔT = nCVΔT + 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
 
  • #4
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134
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 :redface: .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 nCPΔT
 
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  • #5
19,549
3,918
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 nCPΔT
Oh, sorry. I misread the Cp as Cv. I think it would be worthwhile adding the words "at constant pressure" to Case 1.

Chet
 
  • #6
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134
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 Cp as Cv. I think it would be worthwhile adding the words "at constant pressure" to Case 1.

Chet
Right.

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