Question #133330

- Calculate the internal energy and enthalpy of 1 kg of air occuping 0.05 m (cubic) at 20 bar. If the internal energy is increased by 120 kJ as the air is compressed to 50 bar, calculate the new volume, Cp and Cv.

Expert's answer

Assuming air to be a calorically perfect gas.

R=287J/Kg-K, Cp=1.005KJ/kgK

Cv=0.714 KJ/kgK

Given as: mass(m)=1Kg, Volume (V)=0.05m^{2}

By ideal gas equation:

T=(20x10^{5}x0.05)/287 =348.43 K

Internal energy (U_{1})=mCvT=1x714x3484.3=248.780 k J

If internal energy is increased by 120 kJ

U_{2}=248.78+120=368.78kJ

T_{2}=U_{2}/Cv=516.5K

Given as P_{2}=50x10^{5}Pa

V_{2}=(mRT_{2})/(P_{2})

=(287x0.05x516.5)/(50x10^{5})

=0.001467 m^{3}

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