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Question

In a compressor a mixture of 0.3 kg of carbon dioxide and 0.2 kg of nitrogen is compressed from

P1=1 bar, T1=300 K to P2=3 bar in a polytropic process with n = 1.25.

What is the work of compression in this process?

A
18.14 kJ
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B
27.19 kJ
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C
34.09 kJ
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D
39.31 kJ
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Solution

The correct option is C 34.09 kJ
For an ideal gas, the temperature and pressures at the end states of a polytropic process are related as

T2=T1(P2P1)n1/x=300×(31)0.2=373.72 K

Work of compression is given as

=P1V1P2V2n1=m(R/m)(T1T2)n1

m=mCO2+mN2=0.3+0.2=0.5 kg

nCO2=0.344=0.0068 kmol

nN2=0.228=0.0071 kmol

n=nCO2+nN2=0.0068+0.0071=0.0139 kmol

Now molecular weight of the mixture

=mn=0.50.0139=35.97

Wcomp=0.5×(8.31735.97(300373.72))1.251=34.09 kJ

-ve sign indicates work is done on the mixture.

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