Change of internal energy of an ideal gas

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SUMMARY

The discussion centers on calculating the change of internal energy (Δu) of an ideal gas using the integral formula Δu = ∫ [(a-Ru)+bT+cT^2+dT^3]dT. The correct integration approach involves recognizing that the first term, (a-Ru), is treated as a constant, leading to the integration result of [(a-Ru)T + bT^2/2 + cT^3/3 + dT^4/4]. The final answer provided is 6447 kJ/kmol, which the participants confirm after clarifying the integration process.

PREREQUISITES
  • Understanding of thermodynamics, specifically the concept of internal energy.
  • Familiarity with integral calculus and its application in physics.
  • Knowledge of ideal gas laws and properties.
  • Experience with the specific heat capacity coefficients (a, b, c, d) in thermodynamic equations.
NEXT STEPS
  • Review the principles of thermodynamic internal energy calculations.
  • Practice integration techniques for polynomial functions in thermodynamic contexts.
  • Explore the implications of constant terms in integrals related to physical equations.
  • Investigate the application of ideal gas laws in real-world scenarios.
USEFUL FOR

Students studying thermodynamics, engineers working with gas systems, and anyone involved in energy calculations in physical chemistry.

DevonZA
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Homework Statement


upload_2017-5-16_9-52-57.png


Homework Equations


Δu = ∫ [(a-Ru)+bT+cT^2+dT^3]dT

The Attempt at a Solution



The answer of 6447kJ/kmol is given but I am struggling to get to this answer after integrating the above formula and inserting the given values.

Firstly would the integral of [(a-Ru)+bT+cT^2+dT^3]dT
be:

[(a-Ru)+bT^2/2+cT^3/3+dT^4/4] ?
 
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No. The first term should be (a-Ru)T.
 
mjc123 said:
No. The first term should be (a-Ru)T.

Is this because (a-Ru) is a constant?
eg. ∫1 dx = x
 
Yes
 
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Likes   Reactions: DevonZA
mjc123 said:
Yes

Thank you let me give that a try.
 
upload_2017-5-16_11-12-38.png
 

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