Molecule Kinetics: Calculating Temperature from Speed Upon Moon Re-Entry

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SUMMARY

The discussion focuses on calculating the temperature of nitrogen molecules striking a space vehicle during re-entry at a speed of 4.9E4 km/h. Participants emphasize the use of the kinetic energy equation KE=0.5mv²=kT, where 'm' represents the mass of nitrogen molecules. The mass of a nitrogen molecule (N2) is derived from its molecular weight, with N2 having a molecular weight of 28.0134 u, and the conversion of atomic mass units to kilograms is highlighted. The final solution for temperature T can be obtained by substituting the appropriate values into the kinetic energy equation.

PREREQUISITES
  • Understanding of kinetic energy equations (KE=0.5mv²)
  • Knowledge of Boltzmann's constant (k)
  • Familiarity with molecular weight and atomic mass units
  • Basic principles of thermodynamics related to gas molecules
NEXT STEPS
  • Research the calculation of temperature using kinetic energy equations
  • Learn about the properties of nitrogen molecules (N2) and their molecular weight
  • Explore the significance of Boltzmann's constant in thermodynamic equations
  • Study the conversion of atomic mass units to kilograms for accurate calculations
USEFUL FOR

Students in physics and chemistry, aerospace engineers, and anyone involved in thermodynamic calculations related to molecular kinetics.

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Homework Statement



A space vehicle returning from the Moon enters Earth’s atmosphere at a speed of about 4.9E4 km/h. Molecules (assum nitrogen) striking the nose of the vehicle with this speed correspond to what temperature?

Homework Equations



KE=0.5mv^2=kT
k: constant

The Attempt at a Solution



I'm lost.
 
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Look up the mass of an N2 molecule and Boltzmann's constant, k, put them into your first equation and solve for T. ?
 
Dick said:
Look up the mass of an N2 molecule and Boltzmann's constant, k, put them into your first equation and solve for T. ?

Can't look up mass, only molecular weight. Where mass=#mols*molecular weight.
 
bpw91284 said:
Can't look up mass, only molecular weight. Where mass=#mols*molecular weight.

You can so look up the mass of a single nitrogen atom. It's in the periodic table in atomic mass units. What's an atomic mass unit in kilograms? Can also be looked up.
 
Dick said:
You can so look up the mass of a single nitrogen atom. It's in the periodic table in atomic mass units. What's an atomic mass unit in kilograms? Can also be looked up.

N=14.00674u
1 u ≈ 1.66053886 × 10−27 kg

Then just solve for T with 0.5mv^2=kT?

Thanks,
Brandon
 
Except remember the question says 'molecules' and nitrogen is N2 (two nitrogen atoms).
 
Last edited:

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