Answer to Question #308906 in Civil and Environmental Engineering for Sonnie

Question

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 PV^1.3 =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

Answer 1

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= $\frac{0.675\times0.287\times553.15}{14\times10^3}$ = 0.0077

V₂= 4V₁= 4$\times$10^-3 = 0.03m³

(b.) P₁V₁ⁿ = P₂V₂ⁿ

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

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

T_{2 =} $\frac{P_2}{P_1}\times\frac{V_2}{V_1}\times(T_1)$

T_{2 =} $\frac{2.3\times10^3}{14\times10^3}\times\frac{4}{1}\times553.15$

T₂ = 363.499 - 280 = 83.5°C

T₂ = 83.5°C