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)`
C. `R`
D. `(23)/(7)R`

Answer

D

Explanation

d. `C_(v)` for hydrogen `= 5 R //2, C_(V)` for helium `= 3 R//2, C_(v)` for water vapour `= 6 R//2`
`:. (C_(v))_(max) = (4 xx (5R)/(2) + 2 (3R)/(2) + 1 xx 3R)/(4 + 2 + 1) = (16R)/(7)`
`:. C_(P) + C_(v) + R = (16 R)/(7) + R = (23R)/(7)`