A piston-cylinder device contains an ideal gas mixture of 3 kmol of He gas and 7 kmol of Ar gas at 35°C and 420 kPa. Now the gas expands at constant pressure until its volume doubles. The amount of heat transfer to the gas mixture is
A)5.9 MJ
B)7.3 MJ
C)38 MJ
D)257 MJ
E)64 MJ

Question

Quizplus · Accepted Answer

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N_He=3 "kmol"
N_Ar=7 "kmol"
T1=35+273 "C"
P1=420 "kPa"
P2=P1
"T2=2T1 since PV/T=const for ideal gases and it is given that P=constant"
T2=2*T1 "K"
MM_He=4 "kg/kmol"
MM_Ar=39.95 "kg/kmol"
m_He=N_He*MM_He
m_Ar=N_Ar*MM_Ar
Cp_Ar=0.5203; Cv_Ar = 3122 "kJ/kg.C"
Cp_He=5.1926; Cv_He = 3.1156 "kJ/kg.K"
"For a P=const process, Q=DeltaH since DeltaU+Wb is DeltaH"
Q=m_Ar*Cp_Ar*(T2-T1)+m_He*Cp_He*(T2-T1)
 
"Some Wrong Solutions with Common Mistakes:"
W1_Q =m_Ar*Cv_Ar*(T2-T1)+m_He*Cv_He*(T2-T1) "Using Cv instead of Cp"
W2_Q=N_Ar*Cp_Ar*(T2-T1)+N_He*Cp_He*(T2-T1) "Using N instead of mass"
W3_Q=m_Ar*Cp_Ar*(T22-T1)+m_He*Cp_He*(T22-T1); T22=2*(T1-273)+273 "Using C for T1"
W4_Q=(m_Ar+m_He)*0.5*(Cp_Ar+Cp_He)*(T2-T1) "Using arithmetic averate of Cp"

A Piston-Cylinder Device Contains an Ideal Gas Mixture of 3