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Question 6.245E: A cylinder with a linear spring-loaded piston contains carbo...

A cylinder with a linear spring-loaded piston contains carbon dioxide gas at 300 lbf / in .^{2} with a volume of 2 ft ^{3}. The device is of aluminum and has a mass of 8 lbm. Everything (Al and gas) is initially at 400 F. By heat transfer the whole system cools to the ambient temperature of 77 F, at which point the gas pressure is 220 lbf / in .^{2}. Find the total entropy generation for the process.

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CO _{2}: \quad m = P _{1} V _{1} / RT _{1}=300 \times 2 \times 144 /(35.10 \times 860)=2.862   lbm

 

V _{2}= V _{1}\left( P _{1} / P _{2}\right)\left( T _{2} / T _{1}\right)=2(300 / 220)(537 / 860)=1.703   ft ^{3}

 

\begin{aligned}{ }_{1} W _{2  CO _{2}} =\int PdV &=0.5\left( P _{1}+ P _{2}\right)\left( V _{2}- V _{1}\right) \\=&[(300+220) / 2](1.703-2) \frac{144}{778}=-14.29   Btu\end{aligned}

 

{ }_{1} Q _{2  CO _{2}} = mC _{ V 0}\left( T _{2}- T _{1}\right)+{ }_{1} W _{2}=0.156 \times 2.862(77-400)-14.29=-158.5   Btu

 

{ }_{1} Q _{2  A1 }= mC \left( T _{2}- T _{1}\right)=8 \times 0.21(77-400)=-542.6   Btu

 

System:  CO _{2}+ Al

Entropy Eq.:      m _{ CO _{2}}\left( s _{2}- s _{1}\right)_{ CO _{2}}+ m _{ AL }\left( s _{2}- s _{1}\right)_{ AL }={ }_{1} Q _{2} / T _{0}+ S _{ gen \text { tot }}

 

{ }_{1} Q _{2}=-542.6-158.5=-701.14   Btu

 

\begin{array}{l}m _{ CO _{2}}\left( s _{2}- s _{1}\right)_{ CO _{2}}+ m _{ AL }\left( s _{2}- s _{1}\right)_{ AL }= \\2.862[0.201 \ln (537 / 860)-(35.10 / 778) \ln (220 / 300)] \\+8 \times 0.21 \ln (537 / 860)=-0.23086-0.79117=-1.022   Btu / R\end{array}

 

\begin{aligned}S _{\text {gen tot }} &= m _{ CO _{2}}\left( s _{2}- s _{1}\right)_{ CO _{2}}+ m _{ AL }\left( s _{2}- s _{1}\right)_{ AL }-{}_{1} Q _{2} / T _{0} \\&=-1.022+\frac{701.14}{537}=+ 0 . 2 8 3 7  Btu / R\end{aligned}

 

 

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