Question

A mixture of ideal gases has the following composition by mass:

N2	O2	CO2
60%	30%	10%

If the Universal gas constant is 8314 J/kmol-K, the characteristic gas constant of the mixture (in J/kg.K) is _________.

Answer 1

Concept:

M_T R_m = m₁R₁ + m₂R₂ + m₃R₃ + ..............+ m_nR_n

Rm = (m1R1 + m2R2 + m3R3 + ..............+ mnRn) / M_T   ...................(1)

M_T = m1 + m2 + m₃ +...................+ m_n

R_1, R₂, R₃ are the characteristic gas constant of individual gases.

R_m = Characteristic gas constant of the mixture of gases

R (Characteristic gas constant) = (universal gas constant) / (molecular mass of gas)

R = R_u / M   

Calculation:

Given:

1,2, and 3 represent the gases N2, O2, and CO2 respectively.

m₁ = 0.6M_T, m₂ = 0.3M_T,m₃ = 0.1M_T 

R₁ =  R_u / 28, R₂ =  Ru / 32, R₃ =  Ru / 44

R_u = 8314 J/kmol-k

Using equation 1,

\({R_m} = ({m_1}{R_1} + {m_2}{R_2} + {m_3}{R_3})/{M_T}\;\)

\({R_m} = \frac{{\left( {\frac{{0.6{M_T}{R_u}}}{{28}} + \frac{{0.3{M_T}{R_u}}}{{32}} + \frac{{0.1{M_T}{R_u}}}{{44}}} \right)}}{{{M_T}}}\)

\({R_m} = \frac{{0.6{R_u}}}{{28}} + \frac{{0.3{R_u}}}{{32}} + \frac{{0.1{R_u}}}{{44}}\)

R_m = 274.9961 J/kg-K