Degrees of Freedom and Molar Specific Heats

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SUMMARY

The discussion focuses on the calculation of internal energy increase in a diatomic gas during an isobaric process where 70J of heat is added. The user correctly applies the relationship between heat added and internal energy using the specific heat capacities, concluding that the internal energy increases by 50J. This is validated by the known ratio of specific heats for diatomic gases, Cp/Cv = 7/5. The solution is confirmed as accurate by another participant in the discussion.

PREREQUISITES
  • Understanding of thermodynamic processes, specifically isobaric processes.
  • Familiarity with the concepts of specific heat capacities, Cp and Cv.
  • Knowledge of the degrees of freedom in diatomic gases.
  • Basic algebra for manipulating equations and ratios.
NEXT STEPS
  • Study the derivation of the specific heat capacities for diatomic gases.
  • Learn about the implications of degrees of freedom on heat capacity.
  • Explore the First Law of Thermodynamics and its application in various processes.
  • Investigate the differences between isobaric and isochoric processes in thermodynamics.
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, particularly those focusing on gas laws and heat transfer, as well as educators seeking to clarify concepts related to specific heats and internal energy changes in gases.

mit_hacker
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Homework Statement



We give 70J as heat to a diatomic gas, which then expands at constant pressure. The gas molecules rotate but do not oscillate. By how much does the internal energy of the gas increase.

Homework Equations





The Attempt at a Solution



I did it this way:
Heat added = nCp dT = 70J.
Let Internal energy = nCv dT = x (say).
Dividing both equations, we obtain:
Cp/Cv = 70/x.
But, Cp/Cv is nothing but the ration of speicifc heat which for a diatomic gas is known to be 7/5. So, x = 50J.

Am I correct? the solution is not given in the book!

Thanks a ton in advance!
 
Physics news on Phys.org
It is an isobaric process.

Your answer is 100% correct.
 
Thanks a ton!

Thank-you so very much. I really appreciate it.
 

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