`N` moles of an ideal diatomic gas is contained in a cylinder at temparature `T`. On supplying some heat to cylinder, `(N)/(3)` moles of gas dissociated into atoms while temparature remaind constant. Heat supplied to the gas is

Options

A. `(NRT)/(3)`
B. `(5NRT)/(2)`
C. `(8NRT)/(3)`
D. `(NRT)/(6)`

Answer

D

Explanation

When `(N)/(3)` moles diatonic gas is dissiocsated into
atoms `(2N)/(3)` no.of monoatomic gas is formed
`U_(i) =NxxC_(v)xxT = Nxx(5R)/(2)xxT=(5NRT)/(2)`
`U_(f) =((2N)/(3)xx(5R)/(2)xxT)+((2N)/(3)xx(3R)/(2)xxT)`
`=(8NRT)/(3)`
`DeltaQ=DeltaU = (8NRT)/(3)-(5NRT)/(2)`
`=(NRT)/(6)`