What is the Internal Energy of an Ideal Gas at Given Conditions?

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SUMMARY

The internal energy of an ideal gas can be calculated using the formula U = (3/2)nRT, where U represents internal energy, n is the number of moles, R is the gas constant (8.31451 J/mol·K), and T is the temperature in Kelvin. In the case of 1.4 moles of argon gas at 24 degrees Celsius (297.15 K), the total internal energy is calculated to be approximately 5185.76 J. This formula is derived from the kinetic theory of gases and is applicable for monatomic ideal gases like argon.

PREREQUISITES
  • Understanding of the ideal gas law (PV = nRT)
  • Knowledge of the kinetic theory of gases
  • Familiarity with temperature conversion from Celsius to Kelvin
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of the internal energy formula for ideal gases
  • Learn about the properties of monatomic gases and their behavior
  • Explore the implications of the ideal gas law in real-world applications
  • Investigate the differences between ideal gases and real gases
USEFUL FOR

Students studying thermodynamics, physics enthusiasts, and anyone needing to understand the properties and calculations related to ideal gases.

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Homework Statement



A container of volume 0.72 m^3 contains 1.4 mol of argon gas at 24 degrees C.

Assuming argon behaves as an ideal gas, find the total internal energy of this gas. The value of gas constant is 8.31451 J/mol x K.

Answer in units of J.


Homework Equations



PV=nRT

The Attempt at a Solution



I'm not sure if that's the right formula or not. I don't know which letter would equal the internal energy. Am I missing a formula somewhere?

My teacher isn't going to be here next week, so I'm kind of stuck learning this on my own. I don't have too much of an understanding of it at all. Thanks for the help.
 
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Ok, I found the formula 3/2nRT.

I got 5185.759887 J, and it was right.

I'm not quite sure where this formula came from. Can anyone explain that?
 
Last edited:
I can't remember it off the top of my head. Isn't the formula derived in your textbook?
 

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