Question #138013

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

Expert's answer

Initial pressure(p_{1})=140x10^{3 }Pa

Initial Volume (V_{1})=150 Lit = 0.150 m3

Final volume(V_{2})= 30 Lit=0.030 m3

Final pressure(p_{2})=?

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

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