Question #308906

Perfect Gases

0.675kg of gas at 1.4 MN/m2 and 2800C is expanded to four times the original volume according to the law PV1.3 =C Determine:

(a) the original and final volume of the gas,

(b) the final pressure of the gas

(c) the final temperature of the gas

Take R=0.287Kj/kg K



1
Expert's answer
2022-03-10T10:49:20-0500

m1 = 0.675 kg

p1 = 1.4 MN/m2

T1 = 280°C

 R = 0.287 kJ/kg K,

v2 = 4 V1


p1v1 = mRT1


(a.) v1 = mRT1 / T1


v1= 0.675×0.287×553.1514×103\frac{0.675\times0.287\times553.15}{14\times10^3} = 0.0077


V2= 4V1= 4×\times10-3 = 0.03m3



(b.) P1V1n = P2V2n


P2= P1[V1V2\frac{V_1}{V_2}]n= 14×\times 103kPa[14\frac{1}{4}]1.3 = 2.3×\times103 kPa



(c.) P1V1T1=P2V2T2\frac{P_1V_1}{T_1}= \frac{P_2V_2}{T_2}


T2 = P2P1×V2V1×(T1)\frac{P_2}{P_1}\times\frac{V_2}{V_1}\times(T_1)


T2 = 2.3×10314×103×41×553.15\frac{2.3\times10^3}{14\times10^3}\times\frac{4}{1}\times553.15


T2 = 363.499 - 280 = 83.5°C


T2 = 83.5°C



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Comments

Awuvoe JOSHUA
17.03.23, 20:36

Excellent

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