Thermodynamics: Work Homework on CO2 Expansion

Click For Summary
SUMMARY

The discussion focuses on calculating the work done during a reversible isothermal expansion of two moles of CO2 from 1 L to 60 L at 298 K, using the Van der Waals equation of state. The equation provided is P = nRT/(V − nb) − n²a/V², with specific constants b = 0.04286 L mol⁻¹ and a = 3.658 L² bar mol⁻². The key challenge identified is determining the appropriate volume to use for calculating pressure (P) during the integration process. The correct approach is to integrate the pressure function over the specified volume range from 1 L to 60 L.

PREREQUISITES
  • Understanding of the Van der Waals equation of state
  • Knowledge of thermodynamic work calculations
  • Familiarity with integration techniques in calculus
  • Basic principles of isothermal processes
NEXT STEPS
  • Study the derivation and application of the Van der Waals equation
  • Learn how to perform integration of pressure functions in thermodynamics
  • Explore the concept of reversible processes in thermodynamics
  • Review examples of work calculations in isothermal expansions
USEFUL FOR

Students studying thermodynamics, particularly those tackling gas expansion problems, and educators looking for examples of applying the Van der Waals equation in real-world scenarios.

subtletuna
Messages
4
Reaction score
0

Homework Statement


Consider a reversible isothermal expansion of two moles of CO2 from 1 L to 60 L at 298 K. Assume that CO2 obeys an equation of state P = nRT/(V − nb) − n2a/V 2 with b = .04286 L mol−1 and a = 3.658 L2 bar mol−2.
(a) Calculate W.


Homework Equations



P = nRT/(V − nb) − n^(2)a/V^2

The Attempt at a Solution


dW = -PextdV
W = -P[(int from V1 to V2)dV
= -P(60L-1L)
My issue here is, I don't know how to find P. The Van der Walls gas equation is posted above, my only issue is I don't know which V to use... Initial? Final? The difference of the two?
Thanks for the help!
 
Physics news on Phys.org
P is a function of V (the one given in your problem). You have to integrate THAT function from 1 L to 60 L.
 

Similar threads

Replies
30
Views
5K
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K
Replies
1
Views
2K
  • · Replies 23 ·
Replies
23
Views
12K
Replies
4
Views
4K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
5
Views
3K
Replies
12
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K