`n_(1)` moles of a monoatomic gas are contained in a vessel A of volume `V_(1)` at pressure `P_(1)` and temperature `T_(1).n_(2)` moles of the same gas are contained in a vessel B of volume `V_(2)` at pressure `P_(2)` and temperature `T_(2)`. The two vessels are now connected by a tube. Obtain the expression for common temperature T in the Vessels.

Options

A. `(n_(1)T_(2)+n_(2)T_(1))/(n_(1)+n_(2))`
B. `(n_(1)T_(1)+n_(2)T_(2))/(n_(1)+n_(2))`
C. `(n_(1)T_(1)-n_(2)T_(2))/(n_(1)+n_(2))`
D. `(n_(1)T_(1)+n_(2)T_(2))/(n_(1)-n_(2))`

Answer

B

Explanation

If f = number of degrees of freedom,
Initial total energy = final total energy
`rArr (f)/(2) n_(1)RT_(1)+(f)/(2) n_(2)RT_(2) =(f)/(2)(n_(1)+n_(2))RT " " ........(1)`
Here f =3 (monoatomic gas)
Equation (1) gives
`T=(n_(1)T_(1)+n_(2)T_(2))/(n_(1)+n_(2))`