Equation for molar specific heat

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SUMMARY

The discussion focuses on deriving the expression for the molar specific heat at constant volume for a mixture of n_1 moles of a monatomic gas and n_2 moles of a diatomic gas. The molar specific heat for the monatomic gas is established as C_v = 3/2R, while for the diatomic gas, it is C_v = 5/2R. The correct expression for the molar specific heat of the mixture is derived by combining these values, resulting in C_v(mixture) = (3/2n_1 + 5/2n_2)R/(n_1 + n_2).

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  • Understanding of molar specific heat concepts
  • Familiarity with the ideal gas law
  • Knowledge of thermodynamic principles
  • Basic algebra for manipulating equations
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  • Study the derivation of molar specific heat for different gas types
  • Learn about the ideal gas law and its applications
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Metalsonic75
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n_1 moles of a monatomic gas and n_2 moles of a diatomic gas are mixed together in a container. Derive an expression for the molar specific heat at constant volume of the mixture. Expression must be in terms of n_1, n_2, and the gas constant R.

I know that the molar specific heat of the entire mixture is Q = C_v(n_1+n_2)*delta(T). and my physics professor told me that I can use the equation Q = 3/2nR*delta(T) and set it equal to C_v(n_1+n_2)*delta(T) and somehow use that to solve for something, but I'm not sure what I can solve for. I keep getting C_v = 3/2R, but when I plug that in, the equation doesn't work ( 3/2R(n_1+n_2) is incorrect ). I would appreciate some help. Thanks
 
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The molar specific heat of a diatomic gas is 5/2R. Does this help?
 
Got it! Thanks!
 

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