Find the molar specific heat for each gas.

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SUMMARY

The discussion centers on calculating the molar specific heat for a mixture of two ideal gases: one atomic and one diatomic, contained in a 1-liter calorimeter. After adding 10J of thermal energy, the temperature of the mixture increases by 14.2 K. The ideal gas law, pV=nRT, was utilized to determine the number of moles (n=0.419) at 1 atm pressure. The molar specific heat is derived from the equation C_v = (∂U/∂T)_v = (3/2)(f/2)R, where f represents the degrees of freedom.

PREREQUISITES
  • Understanding of the ideal gas law (pV=nRT)
  • Knowledge of thermal energy transfer and temperature change
  • Familiarity with molar specific heat concepts
  • Basic principles of statistical mechanics
NEXT STEPS
  • Study the derivation of molar specific heat for different types of gases
  • Learn about the degrees of freedom for atomic and diatomic gases
  • Explore the relationship between internal energy and heat transfer
  • Investigate the application of the ideal gas law in calorimetry
USEFUL FOR

Students studying thermodynamics, physicists interested in gas behavior, and anyone involved in calorimetry experiments.

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Homework Statement


A mixture of two ideal gases, the first one atomic and the second two atomic are put in normal conditions in a calorimeter with volume 1 liter hermetically closed. After it is given 10J thermal energy the mixture temperature is grown 14.2 K. Find the molar specific heat for each gas.

Homework Equations


pV=nRT

The Attempt at a Solution


I found the n=0.419 with that formula taking the pressure 1atm).What should I do then? What is molar specific heat? I think it is delta U, but how does it relate to to the 10J heat?
 
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If you have one atomic gas then n=0.042. In classical statistic mechanics molar specific heat for gasses is:
$$ C_v = \left(\frac{\partial{U}}{\partial{T}}\right)_v = \frac{3}{2}\frac{f}{2}R $$
where f is the number of freedom degrees, so don't understand what is the question.
 

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