The energy produced by the de`-`excitation of `(1)/(1000)` moles of `H -` atoms from `1^(st)` excited to ground state is supplied to `2` moles of an ideal gas. `10` litres of that gas at `27^(@)C` are allow to expand reversibly & isothermally. The final volume fo the gas will be

Options

A. `15l`
B. `- 20l`
C. `- 25l`
D. `- 30l`

Answer

B

Explanation

`DE = -2.18 xx 10^(-18) [1 - (1)/(4)]`
`= -2.18 xx 10^(-18) xx (3)/(4)` J/ atom
`= -2.18 xx 10^(-18) xx (3)/(4) xx 6.022 xx 10^(20)` Jouls for `(1)/(100)` moles
`= -2.18 xx (3)/(4) xx 6.022 xx 10^(2)J`
`= -3940 J`
Now for isothermal expansion `DeltaU = 0`
`:. dq = -dw`
so `w = -2.303 nRT log. (v_(2))/(v_(1))`
`- 39400 = -2.303 xx 2 xx 8.314 xx 300 xx "log" (v_(2))/(v_(1))`
`"log"(v_(2))/(v_(1)) = (39400)/(11488.3)`
`"log" (v_(2))/(10) = 0.3`
or `(v_(2))/(10) = 2`
`v_(2) = 20` litre