Chemical Forums

Please login or register.

Login with username, password and session length

Sponsored links

Pages: [1]   Go Down

Author Topic: Adiabatic Process  (Read 3721 times)

0 Members and 1 Guest are viewing this topic.

gingi85

  • Regular Member
  • ***
  • Mole Snacks: +0/-1
  • Offline Offline
  • Posts: 46
Adiabatic Process
« on: November 17, 2007, 08:28:36 AM »

In the derivation of the continuous formula for an adiabatic process we say:

dU=dW=CvdT

I'm having trouble understanding this, because, as far as I understood, dU=CvdT is only true of a process where the volume remains constant. As follows:

dU = dQ + dW = dQ -PexdV

Since the volume remains constant,

dV = 0

dU = dQ

We then define,

Cv = dQ/dT]v

and therefore

dU = CvdT

But this should only hold true for a process of constant volume, no? What am I missig?
Logged

Yggdrasil

  • Retired Staff
  • Sr. Member
  • *
  • Mole Snacks: +482/-21
  • Offline Offline
  • Gender: Male
  • Posts: 3199
  • Physical Biochemist
Re: Adiabatic Process
« Reply #1 on: November 17, 2007, 10:44:28 AM »

For an ideal gas, we can write the internal energy, U, as a function of temperature and volume.

U = U(T,V)

From this expression, we can obtain the following differential:

dU = (dU/dT)vdT + (dU/dV)TdV

Note that Cv = (dU/dT)v by definition.
In addition, (dU/dV)T = 0 because the internal energy of an ideal gas depends only on its temperature.

Therefore, we get:

dU = CvdT

This equation works in all cases (but only for ideal gases.  If (dU/dV)T is not zero, this does not hold).

dq = CvdT is only valid for constant pressure processes, however.
Logged

Pages: [1]   Go Up
 

Mitch Andre Garcia's Chemical Forums 2003-Present.

Page created in 0.064 seconds with 20 queries.