What is the change in entropy ΔS of the gas?

Click For Summary
SUMMARY

The change in entropy ΔS for two moles of an ideal gas undergoing a reversible isothermal expansion from 3.37×10−2 m³ to 4.29×10−2 m³ at a temperature of 29.6 °C can be calculated using the formula ΔS = nR ln(V2/V1). The ideal gas law, pV=nRT, is essential for deriving the necessary expressions. The integral W=∫V2V1 pdV is not required for calculating ΔS directly, but understanding the relationship between pressure, volume, and temperature is crucial for manipulating the integrand correctly.

PREREQUISITES
  • Understanding of the ideal gas law (pV=nRT)
  • Knowledge of entropy and its calculation in thermodynamics
  • Familiarity with logarithmic functions and their properties
  • Basic calculus, particularly integration techniques
NEXT STEPS
  • Learn how to derive the entropy change formula for isothermal processes
  • Study the application of the ideal gas law in different thermodynamic processes
  • Explore advanced integration techniques relevant to thermodynamic calculations
  • Investigate the implications of entropy changes in real-world gas expansions
USEFUL FOR

Students studying thermodynamics, physics enthusiasts, and anyone looking to deepen their understanding of entropy and ideal gas behavior in isothermal processes.

kolua
Messages
69
Reaction score
3

Homework Statement


Two moles of an ideal gas undergo a reversible isothermal expansion from 3.37×10−2m3 to 4.29×10−2m3 at a temperature of 29.6 ∘C.

What is the change in entropy ΔS of the gas?

Homework Equations


pV=nRT

The Attempt at a Solution


W=∫V2V1pdV,

I don't know how to use this integral. And is it necessary to use this integral here? It seems like it is making the calculation more complicated than it should be. I have no other idea on how to approach this question. Please give me some hints!
 
Physics news on Phys.org
Hint: In the integration, P=nRT/V
 
You're on the right path. Note that the integral should be
\int_{V_{1}}^{V_{2}} \frac{PdV}{T}
Manipulate the integrand using the ideal gas equation of state to obtain an expression in terms of the variable of integration (i.e. the volume) and then do the integral.
 

Similar threads

Replies
1
Views
2K
  • · Replies 33 ·
2
Replies
33
Views
3K
Replies
1
Views
2K
Replies
10
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
10
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 10 ·
Replies
10
Views
23K
  • · Replies 5 ·
Replies
5
Views
3K