How Is the Internal Energy of Helium Calculated in an Ideal Gas Scenario?

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SUMMARY

The internal energy of helium in an ideal gas scenario can be calculated using the equation Eint = 3/2nRT, where n represents the number of moles, R is the universal gas constant (8.31451 J/Kmol), and T is the temperature in Kelvin. For 2.79 moles of helium at 5°C (278.15 K), the total thermal energy can be determined. The alternative equation Eint = 3/2NKbT is applicable for individual molecules, where Kb is Boltzmann's constant (1.38066 x 10^-23 J/K). Both equations yield the same result, differing only by the scale of measurement.

PREREQUISITES
  • Understanding of ideal gas laws
  • Familiarity with the universal gas constant (R)
  • Knowledge of Boltzmann's constant (Kb)
  • Basic thermodynamics concepts
NEXT STEPS
  • Calculate internal energy for different gases using Eint = 3/2nRT
  • Explore the relationship between temperature and internal energy in ideal gases
  • Learn about Avogadro's number and its significance in gas calculations
  • Investigate real gas behavior versus ideal gas assumptions
USEFUL FOR

Students in physics or chemistry, researchers in thermodynamics, and professionals working with gas laws and energy calculations will benefit from this discussion.

jdog6
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A tank of volume 0.413 m3 contains 2.79 mol
of helium gas at 5C. Assume that the helium
behaves like as an ideal gas.
The universal gas constant is
8.31451 J/Kmol, and Boltzmann's constant
is 1.38066 x10^-23 J/K.
Find the total thermal energy of the system.
Answer in units of J.
Would the right equation be Eint = 3/2NKbT =3/2nRT ?
 
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Both are the same. The first (with "Boltzmann" constant) is for use when observing idividual atoms or molecules. N=number of molecules.

The second is for use when observing large quantities. n = number of moles. The only difference between R and k is Avogadro's number (k = R/N)

So, what are you given. number of molecules, or number of moles?

Oh yeah, what's the temperature? Are you ABSOLUTELY sure?
 

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