Thermodynamics - Internal Energy in Isochoric and Isobaric Processes

  • Thread starter tanooj
  • Start date
  • #1
3
0

Main Question or Discussion Point

Assuming that the gas in these processes is an ideal one, is the change in internal energy in an isochoric process (volume remaining constant) the same as the change in internal energy of isobaric process (pressure remaining constant)? Mathematically I can derive that they're equivalent, but what's the physical reason behind that? Does it have something to do with the temperature of the gas? My reasoning is this: if you start from the a point on a PV diagram (I'll call it A) and move up in an isochoric process to a point B, and then starting from A if you move right to a point C in an isobaric process, you end up at an isotherm that both A and C lie on if you add equal amounts of heat Q in both AC and AB, and that's why their changes in internal energy are the same. Is my reasoning correct?
 

Answers and Replies

  • #2
Philip Wood
Gold Member
1,221
75
In an ideal gas, internal energy, U, depends only on temperature. For n moles of ideal gas, U = ncvT
in which cv is the ‘molar heat capacity at constant volume’.

So ΔU will be the same in an isochoric or isobaric change, provided that ΔT is the same.

What you've said is good up to "you end up at an isotherm that both A and C lie on". After that you go adrift. In the isobaric process you have to put in more heat for the same temperature change than in the isochoric change. The reason for this is that in the isobaric change the gas does external work (pushing out a piston or whatever) and this, as well as the rise in internal energy, has to be paid for as heat. For the isochoric change there's no external work done, so only ΔU has to be paid for by heat.
 
Last edited:
  • #3
3
0
Oh all right that makes sense. Thanks!
 

Related Threads on Thermodynamics - Internal Energy in Isochoric and Isobaric Processes

Replies
5
Views
4K
Replies
3
Views
1K
Replies
3
Views
3K
Replies
3
Views
2K
  • Last Post
Replies
1
Views
1K
Replies
7
Views
3K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
976
Replies
8
Views
2K
  • Last Post
3
Replies
61
Views
3K
Top