Question

378 𝑙𝑝𝑠 of air is isothermally compressed at 27℃ and 1379 𝑘𝑃𝑎𝑎; 𝑝2 = 4136 𝑘𝑃𝑎𝑎. For both nonflow and steady-flow (𝑉1 = 23 𝑚 𝑠 , 𝑉2 = 46 𝑚 𝑠 , ∆𝑃 = 0) processes, compute (a) ∫ 𝑝𝑑𝑉 𝑎𝑛𝑑 − ∫ 𝑉𝑑𝑝 (b) ∆𝑈, ∆𝐻, 𝑎𝑛𝑑 ∆𝑆 (c) 𝑊 𝑎𝑛𝑑 𝑄 

Answer 1

a)

$\int pdV=\nu RT=572.5~kJ,$

$\int Vdp=p_2V_2-p_2V_2=-575.2~kJ,$

b)

$\Delta U=p\Delta V-V\Delta p=4.8~kJ,$

$\Delta H=\Delta U+pV=572.5~kJ,$

$\Delta S=\frac UT=1.9085~\frac{kJ}K,$

c)

$W=2\Delta U=9.6~kJ,$

$Q=pV=575.2~kJ.$