Answer to Question #138013 in Mechanical Engineering for dilan

Question

The water vapor is pressurized at first 140 kPa and its volume is 150 liters, then compressed so that the volume becomes 30 liters following the law pV1,2 = C. determine the work and final pressure

Answer 1

Initial pressure(p₁)=140x10³ Pa

Initial Volume (V₁)=150 Lit = 0.150 m3

Final volume(V₂)= 30 Lit=0.030 m3

Final pressure(p₂)=?

Gas undergoes a polytropic process given by pV^1.2 =constant

Therefore, for process 1-2 we can write,

$p_1 \times {V_1}^{1.2} = p_2 \times {V_2}^{1.2}$

${P_2}=\frac { p_1 \times {V_1}^{1.2} }{{V_2}^{1.2}}$

${P_2}=\frac { 140 \times {0.150}^{1.2} }{{0.030}^{1.2}}$ =965.81 kPa

The work done during poly tropic process is given by

$W=\frac {p_1 \times V_1-p_2 \times V_2}{n-1}$

$W=\frac {(140\times (0.150)-(965.81)\times (0.030)}{1.2-1}$ =-38.8715 kJ (-ve sign indicates work done on the gas)

Work done on the gas is W=39.8715 kJ