Change of internal energy of an ideal gas

AI Thread Summary
The discussion revolves around calculating the change of internal energy of an ideal gas using the integral Δu = ∫ [(a-Ru)+bT+cT^2+dT^3]dT. The user is attempting to integrate the formula but is confused about the correct form of the integral, particularly regarding the first term, which should be treated as a constant multiplied by T. Clarification is sought on whether the first term should indeed be (a-Ru)T. The user expresses gratitude for the guidance and plans to try the suggested approach. The conversation highlights the challenges of integrating complex equations in thermodynamics.
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 DevonZA
mjc123 said:
Yes

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