100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
THERMODYNAMICS: ADIABATIC PROCESSES $6.45   Add to cart

Class notes

THERMODYNAMICS: ADIABATIC PROCESSES

 2 views  0 purchase
  • Course
  • Institution
  • Book

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

Preview 2 out of 6  pages

  • November 13, 2022
  • 6
  • 2022/2023
  • Class notes
  • Dr ray
  • All classes
avatar-seller
1


Work in reversible adiabatic processes



From : dw = -PdV (1)


Overall work is defined by:



𝑤 = − ∫ 𝑃𝑑𝑉

(2)
For an adiabatic reversible process (expansion or compression) the governing formula is:

𝑃𝑉 𝛾 = 𝐶


Rearranging in terms of P:

𝐶
𝑃=
𝑉𝛾
Followed by substitution in (2):
𝑉2
1
𝑤 = −𝐶 ∫ 𝑑𝑉
𝑉1 𝑉𝛾

(3)
Solve integral by applying power rule:


∫ n
x n+1
ax dx = a +C
n+1

𝑉2
𝑤 = −𝐶 ∫ 𝑉 −𝛾 𝑑𝑉
𝑉1

(4)
1 𝑉
𝑤 = −𝐶[ 𝑉 1−𝛾 ]𝑉21
1−𝛾
(5)

, 2


1 1
𝑤 = −𝐶[ 𝑉2 1−𝛾 − 𝑉 1−𝛾 ]
1−𝛾 1−𝛾 1


𝐶 1−𝛾
𝑤=− [𝑉2 − 𝑉1 1−𝛾 ]
1−𝛾

(6)
You may further want to get rid of the negative sign. Since 1-γ = -(γ-1), the equation then
changes to:


𝐶 1−𝛾
𝑤= [𝑉 − 𝑉1 1−𝛾 ]
𝛾−1 2

(7)
Work can also be evaluated in terms of the temperature change, since


𝑑𝑈 = 𝑑𝑤
(8)
𝑑𝑤 = 𝑛𝐶𝑉 𝑑𝑇


𝑇2
𝑤 = 𝑛𝐶𝑉 ∫ 𝑑𝑇
𝑇1



𝑤 = 𝑛𝐶𝑉 (𝑇2 − 𝑇1 )
(9)
It is assumed that CV is constant.


Example1: Work of adiabatic reversible expansion
Consider the adiabatic, reversible expansion of 0.020 mol Ar, initially at 25°C, from
0.50 dm3 to 1.00 dm3. Calculate the work of expansion.
Given: Cvm = 12.48 J K-1 mol-1


Method 1: Use of
𝐶 1−𝛾
𝑤= [𝑉2 − 𝑉1 1−𝛾 ]
𝛾−1

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

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

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

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 $6.45. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

83637 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$6.45
  • (0)
  Add to cart