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Question

A mixture of ideal gases has the following composition by mass:
N2 O2 CO2
60% 30% 10%
If the universal gas constant 8314J/kmolK, the characteristic gas constant of the mix
  1. 274.86

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Solution

The correct option is A 274.86
Equation state forN2,

pN2V=mN2RN2T

or pN2VT=mN2RN2\)

Where RN2=¯¯¯¯RMN2

pN2VT=mN2¯¯¯¯RMN2...(i)

SImilarly for O2 and CO2

pCO2VT=mO2¯¯¯¯RMO2....(ii)

and pCO2VT=mCO2¯¯¯¯RMCO2...(iii)

Adding equation (i), (ii) and (iii), we get

VT(pN2+pO2+pCO2+)=mN2¯¯¯¯RMN2+mO2¯¯¯¯RMO2+mCO2¯¯¯¯RMCO2

VT+p=(mN2MN2+mO2MO2+mCO2MCO2)¯¯¯¯R...(iv)

where, pressure of mixture

p=pN2+pO2+pCO2

Equation of state for mixture of ideal gas

pV=mRTor

pVT=mR...(v)

Equating ECs (iv) and (v) we get

mR=(mN2MN2+mO2MO2+mCO2MCO2)¯¯¯¯R

mR=(0.60mMN2+0.30mMO2+0.1mMCO2)¯¯¯¯R

or R=(0.60MN2+0.30MO2+0.1MCO2)¯¯¯¯R

==(0.6028+0.3032+0.1044)×8314

=(0.02142+0.00937+0.00227)×8314

=0.03306×8134

=274.86J/kgK

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