Question

Say & lb/sec of CO₂ gas are com .2 H pressed polytropically (pV¹² = C) from Pi =. 15 psia, ₁ 140°F to 1₂ = 440°F. As suming ideal gas action, find P2, W, Q, AS (a) as a nonflow process, (b) as a steady flow process where AP = 0, AK = 0.

Answer 1

Solution;

Given;

$P_1=15psia=103.421kPa$

$T_1=140°F=333.15K$

$T_2=440°F=499.82K$

$\dot{m}=1lb/s=0.4536kg/s$

For carbon dioxide;

$R=0.1889kJ/kgK$

$\frac{P_1}{P_2}=(\frac{T_1}{T_2})^{\frac{n}{n-1}}$

$\frac{103.421}{P_2}=(\frac{333.15}{499.82})^{\frac{1.2}{0.2}}$

$P_2=1179.09kPa$

Work;

$W=\frac{mR(T_2-T_1)}{n-1}$

$W=\frac{0.4536×0.1889(499.82-333.15)}{1.2-1}$

$W=71.41kW$

Heat;

$Q=W+\Delta u$

$\Delta u=mc_v(T_2-T_1)$

$0.2c_v=R$

$c_v=0.9445kJ/kgK$

$\Delta u=0.4536×0.9445(499.82-333.15)=71.41kW$

$Q=W+\Delta u=142.82kW$