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. monoatomic
B. diatomic
C. triatomic
D. tetra atomic

Answer

b

Explanation

(b) `C_(v)` of gas `A =(3)/(2)R+(3)/(2)R+6R=9R`
Let `C_(v)` of gas` B = X `
Heat lost by gas `A =7xx9Rxx(T-(5T)/(6))`
Heat gained by gas `B=6X((5T)/(6)-(T)/(3))`
`implies " "63R((T)/(6))=6X((T)/(2))=X=(7)/(2)R,`
`:.` gas is diatomic