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 kJFor an ideal gas, the temperature and pressures at the end states of a polytropic process are related as T2=T1(P2P1)n−1/x=300×(31)0.2=373.72 K Work of compression is given as =P1V1−P2V2n−1=m(R/m)(T1−T2)n−1 m=mCO2+mN2=0.3+0.2=0.5 kg nCO2=0.344=0.0068 k−mol nN2=0.228=0.0071 k−mol ∑n=nCO2+nN2=0.0068+0.0071=0.0139 k−mol Now molecular weight of the mixture =m∑n=0.50.0139=35.97 ∴ Wcomp=0.5×(8.31735.97(300−373.72))1.25−1=−34.09 kJ -ve sign indicates work is done on the mixture.

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