Answer to Question #308896 in Civil and Environmental Engineering for Sonnie

Question

0.1m³ of gas is compressed from pressure of 120KN/m² and temperature 25⁰C to a pressure of 1.2MN/m² according to the law PV^1.2 = constant.

Determine,

(a) The work transferred during the compression,

(b) The change in internal energy,

(c) The heat transferred during the compression

Assume , c_v=0.72kJ/kgK         and           R=0.285KJ/kgK

Answer 1

c_v=0.72kJ/kgK

R=0.285KJ/kgK

a.) $work = − P Δ V$

For PV$^{\gamma}$ = constant

work done by the gas = $\frac{(P_2V_2-P_1V_1)}{(1-\gamma)}$ where $\gamma = 1.2$

for calculation of $P_2 = P_1(\frac{V_1}{V_2})^{1.2}$

$= 1.2(\frac{1.2}{120})^{120}$

P₂= 3.175

hence work done=$\frac{3.175\times1\times0.05}{1.2-1}$

work done by gas = 0.794 m³

b.) $ΔU = Q − W$

$ΔU =$ 18J - 7.125J

= 10.875 J

c.) $ΔH=qp$

= $\frac{25\times1.2}{120}$

= $\frac{30}{120}$

= 0.25