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

\(\frac{23}{7}R\)

C_v_hydrogen = \(\frac{5}{2}R\)

C_v_helium = \(\frac{3}{2}R\)

C_v_{water vapour} = \(\frac{6}{2}R\)

\(\Rightarrow C_{v_{mix}} = \frac{4*\frac{5R}{2} + 2*\frac{3R}{2} + 1*3R}{4+2+1} = \frac{16}{7}R\)

\(\Rightarrow C_P = C_V + R\)

\(\Rightarrow C_P = \frac{16}{7}R + R = \frac{23}{7}R\)