Three kilograms of an ideal gas with R = 204 J/kg-K and k = 1.667 have 316 kJ of heat added during an isobaric process. The initial temperature is 38oC. Determine (a) Wnf, (b) U, (c) S.
Cp=kRk−1=510 Jkg⋅K,C_p=\frac{kR}{k-1}=510~\frac{J}{kg\cdot K},Cp=k−1kR=510 kg⋅KJ,
T2=T1+QmCp=518 K,T_2=T_1+\frac Q{mC_p}=518~K,T2=T1+mCpQ=518 K,
CV=Rk−1=306 Jkg⋅K,C_V=\frac{R}{k-1}=306~\frac{J}{kg\cdot K},CV=k−1R=306 kg⋅KJ,
ν=Cp−CVR=1 mol,\nu=\frac{C_p-C_V}{R}=1~mol,ν=RCp−CV=1 mol,
a)
A=νRΔT=42 kJ,A=\nu R\Delta T=42~kJ,A=νRΔT=42 kJ,
b)
U=Q−A=274 kJ,U=Q-A=274~kJ,U=Q−A=274 kJ,
c)
S=mCplnT2T1=780 JK.S=mC_p\ln\frac{T_2}{T_1}=780~\frac JK.S=mCplnT1T2=780 KJ.
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