Four moles of hydrogen, 2 moles of helium and 1 mole of water form an ideal gas mixture. What is the molar specific heat at constant pressure of mixture ?

Options

A. `(16)/(7)R`
B. `(7 R)/(16 R)`
C. R
D. `(23)/(7) R`

Answer

D

Explanation

`C_(v)` for hydrogen `=(5R)/(2),C_(v)` for helium = `(3R)/(2)`
`C_v` for water vapour = `(6R)/(2)`
`:. [C_(v)]_(mix) = (4xx(5R)/(2)+2(3R)/(2)+1xx3R)/(4+2+1) = (16R)(7)`
`:. C_(p)+C_(v)+R = (16R)/(7)+R = (23R)/(7)`.