The notes are for the thermodynamics in chemistry and chemical engineering. They explain the adiabatic processes in detail and also they consists of worked examples and self test exercises
Unit 5
The internal energy of an ideal gas
Joule experiment
Setup: Two flasks (A and B) are totally immersed in a water bath, which is
surrounded by a thermally insulated wall. A thermometer is in contact with the water
bath.
flask A contains gas at high pressure and separated by valve (in closed
position) from flask B, which is completely evacuated
Valve is opened, and gas would expand against the vacuum while
temperature is monitored
Result: No temperature change was observed
Conclusion: q= 0 and w = 0 (dw = -PextdV , Pext = 0)
ΔU = q + w = 0
(1)
A total differential (dU) can be setup for this system that evaluated volume change
and temperature change:
𝜕𝑈 𝜕𝑈
𝑑𝑈 = ( ) 𝑑𝑉 + ( ) 𝑑𝑇 = 0
𝜕𝑉 𝑇 𝜕𝑇 𝑉
(2)
, Effect on U when
Step 1: changing V while keeping T constant
Step 2: changing T while keeping V constant
U
(1) dU = 0
(2) T
V
Rearrangement of equation 2:
𝜕𝑈 𝜕𝑈 𝜕𝑇
( ) = −( ) ( )
𝜕𝑉 𝑇 𝜕𝑇 𝑉 𝜕𝑉 𝑈
(3)
From Joule experiment: temperature did not change on expansion of gas, therefore
𝜕𝑇
( ) =0
𝜕𝑉 𝑈
This implies from equation 3 that:
𝜕𝑈
( ) =0
𝜕𝑉 𝑇
For an ideal gas, the internal energy is independent of volume.
𝜕𝑈
( ) = 𝜋𝑇
𝜕𝑉 𝑇
𝜋 𝑇 = internal pressure= 0 for ideal gas
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller joseph2001. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.63. You're not tied to anything after your purchase.