Answer to Question #115770 in Mechanical Engineering for Smith

Question

A closed tank contains 100 lbs of air at a pressure of 200 psia and a temperaure of 180 0F. The air is subsequently cooled to 80 0F. Find the: a.) the initial specific volume, ft3/lbm; b.) the volume of the tank, ft3; c.) the final specific volume, ft3/lbm; d.) the final pressure, psia.

Answer 1

Pressure= 200 psia, Air present =100 lbs,$T_1= 180 ^oF, T_2= 80^oF,$

(a) Specific Volume,

$P_1V_1=RT_1$

$200\times V= 53.33\times (180+460)$

$V=170.656$ $ft^3$/lbm

(b)

Volume of the tank ,

V= $\frac {170.656 \times 100}{60}=284.426 ft^3$

(c) for the final specific volume

$P_2V_2=RT_2$

$V_2= \frac{ 53..33\times (80+460)}{200}=143.991$

(d)

Final pressure

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

P2=333.33 psia