Question # If one mole of a monoatomic gas ( (gamma=5 / 3) ) is mixed with one mole of a diatomic gas ( (gamma=7 / 5) ), the value of ( gamma ) for the mixture is.

# If one mole of a monoatomic gas ( (gamma=5 / 3) ) is mixed with one mole of a diatomic gas ( (gamma=7 / 5) ), the value of ( gamma ) for the mixture is.

(a) 1.40

(b) 1.50

(c) 1.53

(d) 3.07

Solution

( gamma_{1}=frac{5}{3} ) means gas is monoatomic or ( C_{V_{1}}=frac{3}{2} R )

( gamma_{2}=frac{7}{5} ) means gas is diatomic or ( C_{V_{2}}=frac{5}{2} R )

( C_{V} ) (of the mixture) ( =frac{n_{1} C_{V_{1}}+n_{2} C_{V_{2}}}{n_{1}+n_{2}}=frac{(1)left(frac{3}{2} Rright)+(1)left(frac{5}{2}right) R}{1+1}=2 R )

( C_{p}( ) of the mixture ( )=C_{V}+R=3 R ) ( therefore gamma_{text {mixture }}=frac{C_{p}}{C_{V}}=frac{3 R}{2 R}=1.5 )