CHEN 354- HW # 4- Due Friday, February 19, 2010
Problem 1. Methane, hydrogen, and propane, all ideal gases, are mixed together in equal parts by
mass to create a new fuel gas. The gas is then adiabatically compressed from 10oC to 0.1 m3 at 2
MPa, 25oC. Determine the work required for the compression process.
Solution:
Given: mfCH4 = mfH2 = mfC3H8 = 0.333. (Equal parts by mass.)
T1 = 10oC, V2 = 0.1 m3, p2 = 2 MPa, T2 = 25oC.
The process is adaiabatic (Q = 0), and we will assume that there is no change in kinetic or
potential energy. Therefore, for this closed system, the first law gives
W = -m (u2 - u1) = m cv (T2 - T1)
The constant volume specific heat of the mixture, is the sum of the mass fractions of each
components times their specific heat of each component. If we assume that the gases have
constant specific heats,
cv = [(mf)(cv)]CH4 + [(mf)(cv)]H2 + [(mf)(cv)]C3H8
cv = (0.333)(1.709) + (0.333)(10.19) + (0.333)(1.502) = 4.46 kJ/kg-K
The molecular mass of the mixture can be found by taking the inverse of the sum of the mass
fractions divided by the molecular mass of each component. This yields M = 5.13 kg/kmole. The
gas specific ideal gas constant is then R = Ru/M = 1.62 kJ/kg-K. The mass of the mixture can
then be found from the ideal gas law at the second state:
m = pV/RT = (2000 kPa)(0.1 m3)/((1.62 kJ/kg-K)(298 K) = 0.414 kg.
The work used to compress the gas is then
W = - (0.414 kg)(4.46 kJ/kg-K)(25 - 10)K = -27.7 kg