Answer to Question #131304 in Mechanical Engineering for syahmi asyraaf

Question

Calculate the internal energy and enthalpy of 1kg air occupying 0.05m3 volume at 20 bars. If the internal energy is increased by 120 kJ as the air is compressed to 50 bars, calculate the new volume occupied by 1 kg of air.

Answer 1

We will assume that gas is ideal. So, the internal energy of air

U=m/MC_VT

For air $M=28.96 \cdot 10^{-3}kg/mol$,and $C_V=\frac{i}{2}R=\frac{5}{2}\cdot 8.31\approx20.8\frac {J}{mol\cdot K}$

U = 1/28.96*10^-3 *20.8*293 = 210442J

The enthalpy of air

H = U + pV = 210442 + 2*10^6*0.05 = 310442J

Change in U = m/M cv (t2-t1) = 120000*28*96*10^3/(1*20*8)+293 = 460k

V2 = 2*10^6*0.05*460/293*5*10^6 = 0.031m^3