Answer to Question #133330 in Mechanical Engineering for lucky mojeremane

Question

1. 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.

Answer 1

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)=0.05m²

By ideal gas equation:

$\frac{P \times V }{Rm}=T$

T=(20x10⁵x0.05)/287 =348.43 K

Internal energy (U₁)=mCvT=1x714x3484.3=248.780 k J

If internal energy is increased by 120 kJ

U₂=248.78+120=368.78kJ

T₂=U₂/Cv=516.5K

Given as P₂=50x10⁵Pa

$\frac{P \times V }{Rm}=T$

V₂=(mRT₂)/(P₂)

=(287x0.05x516.5)/(50x10⁵)

=0.001467 m³