Question

Equal volumes of monoatomic and diatomic gases of same initial temperature and pressure are mixed.What will be the ratio of sprcific heats of the mixture(Cp/Cv)?

Answer 1

Internal energy may be expressed as
U = ν•R•T/(γ-1), and
U = ν• (i/2) •R•T,
where ν is the amount of substance, i is the degrees of freedom (i1 =3, i2 =5),
γ =Cp/Cv -adiabatic index.
From
p• V = ν•R•T, if V1=V2, then ν1= ν2 = ν.
U= U1+U2,
U = ν•R•T/(γ-1) = (ν1+ ν2) •R•T/(γ-1) =2 ν•R•T/(γ-1),
U1+U2 = ν1• (i1/2) •R•T + ν2• (i2/2) •R•T= (i1+i2) •v•R•T/2.
2 ν•R•T/(γ-1) = (i1+i2) •v•R•T/2.
2/(γ-1) =( i1+i2)/2=(3+5)/2 =4
2γ = 3,
γ =1.5