Answer to Question #183769 in Mechanical Engineering for Eric Santos

Question #183769

Assume 5 ft3/s of Hydrogen at 15 psia and 80 oF are compressed during an irreversible adiabatic  process to 90 psia and 522 oF. For a non-flow process determine a) k, b) V2, c) W, d) ΔU and e) ΔS.


1
Expert's answer
2021-04-21T07:04:08-0400

a. "\\frac{T_2}{T_1}=(\\frac{P_2}{P_1})^{\\frac{k-1}{k}}"

"\\frac{545.372}{299.817}=(\\frac{90}{15})^{\\frac{k-1}{k}}"

"\\ln{1.819}=({\\frac{k-1}{k}} )\\ln{6}"

"1.1935k=1.79"

"k=1.5"


b. "P_1V_1^k=P_2V_2^k"

"15(5)^{1.5}=90(V_2)^{1.5}"

"V_2=1.5142 In^3\/s"


c. "\\triangle w = \\frac{P_1V_1-P_2V_2}{k-1}= \\frac{15 \\times 1728 \\times 5 - 90 \\times 1782 \\times 1.5142}{1.5-1}=-211776.76 lb-inch\/s"


d. "\\triangle \\theta = \\triangle w +\\triangle u"

But "\\triangle \\theta =0"

So, "\\triangle w = -\\triangle u"

"\\triangle u=211776.76 lb-inch\/s"


e. "\\triangle s=\\frac{Q}{T}=\\frac{-211776.76}{245.555}=-862.44124 lb-inch \/sK"


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