PLease show your work n1 moles of a monatomic gas and ri2 moles of a diatomic ga

Question

PLease show your work

n1 moles of a monatomic gas and ri2 moles of a diatomic gas are mixed together in a container What is an expression for the molar specific heat at constant volume of the mixture. Express your answer in terms of the given quantities and appropriate constants. Show that your expression has the expected behavior if n1 right arrow 0 n2 right arrow 0. Express your answer in terms of the given quantities and appropriate constants. Enter your answers numerically separated by a comma.

Explanation / Answer

Ans:- A). As we know

for monoatomic gas Cv = 3R/2

for diatomic gas   Cv = 5R/2

As n1 mole of monoatomic gas is mixed so heat content of this gas is n1(3R/2)T

similarly for diatomic gas n2(5R/2)T

Total heat content of mixture Q= n1 (3/2) RT+ n2 (5/2) RT
?Q/?T = [3 n1 + 5 n2]R/2

from relation dU = n .Cv .dT

and from 1st law of thermodynamics dQ = dU + PdV

dV = 0

therefore dQ = dU

so Cv =[1/(n1+n2)] {3 n1 + 5 n2}R/2 ( n = n1 + n2)

         = {3 n1 + 5 n2} R / [2 (n1+n2)]

         = 3 (n1+n2)R / [2 (n1+n2)] + 2 n2 R / [2 (n1+n2)]

         = [3 R / 2 ] + {n2*R / (n1+n2)}

B).expressionn   fro Cv = [3 R / 2 ] + {n2*R / (n1+n2)}

when n1 -> 0     Cv = 3R/2 + R = 5R/2 ( as mixture is diatomic)

when n2 -> 0    Cv = 3R/2 ( ob vious as mixture is now monoatonmic)

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