7 moles of a tetra-atomic non-linear gas 'A' at 10 atm and T K are mixed with 6 moles of another gas B at `(T)/(3)K` and 5 atm in a closed, rigid vessel without energy transfer with surroundings. If final temperature of mixture was `(5T)/(6) K,` then gas B is ? (Assuming all modes of energy are active)

Options

A. monatomic
B. diatomic
C. triatomic
D. tetra atomic

Answer

B

Explanation

`C_(v)` of gas `A= ( 3)/( 2)R + ( 3)/(2) R + 6R = 9R `
Let `C_(v) ` of gas B=X Heat gained by gas `B =6X((5T)/( 6) - ( T)/( 3))`
`rArr 63R((T)/( 6)) =6X ((T)/( 2)) =X= ( 7)/( 2) R,`
`:.` gas is diaatomic