Suppose a diatomic gas gets ionised to a certain extent without any expenditure of heat energy. If the fractional change in the number of moles of the gas be `eta`, then ignoring any enegy loss, the fractional change in the temperature of the gas will be

Options

A. `(-eta)/(eta + 1)`
B. `(-eta)/(eta + 5)`
C. `(eta)/(eta + 1)`
D. `(eta)/(eta + 5)`

Answer

B

Explanation

initially, `E = n_(0)(5/2 RT)` ..(i)
Given `(Delta n)/(n_0) = eta` or `Delta n = eta n_(0)`
Number of moles of `O_(2)` left `(1-n)n_(0)`
Number of moles of `O_(2)` formed = `2Delta n = 2 eta n_(0)`
`:.` Finally, `E = (1-eta )n_(0) ((5RT')/(2))+(2etan_(0))((3RT')/(2))` ..(ii)
Equanting equations (i) and (ii) , `T' = (5T)/(5+eta)`
Fractional change in temperature =` (T')/(T)-1 = (-eta)/(eta+5)`.