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

Options

A. 1.4
B. 1.5
C. 1.53
D. 3.07

Answer

B

Explanation

`({:(C_(v) =(3)/(2) RT),(C_(p) = (5)/( 2)RT):}`for monoatomic gas,
`({:(C_(v) =(5)/(2) RT),(C_(p) = (7)/( 2)RT):}`for diatomic gas,
Thus, for mixutre of 1 mole each,
`C_(v) = ((3)/( 2) RT+( 5)/( 2)RT)/( 2) ` and `C_(p) =((5)/( 2) RT+( 7)/ (2)RT)/( 2)`
Thus, `(C_(p))/( C_(v)) =( 3RT)/( 2RT) = 1.5`