Answer to Question #268189 in Molecular Physics | Thermodynamics for tine

Question

 The height of a cylindrical tank, containing 15 lb of gas at 70 psia and 115 Farenheit, IS TRIPLE ITS DIAMETER; the gas constant is R = 45 ft lbf/lbm R. find.

a) the tankdiameter in ft.

b)the tank height in ft.

Answer 1

W=15 lbm, P= 70 psia, T=115 F, H=3D, R = 45 ft lbf/lbm°R

Volume of cylireler

$V=\frac{π}{4} D^2\times H=\frac{π}{4}D^2\times3D=\frac{3π}{4}D^3\\ V=\frac{3}{4}πD^3$

1F=459.67R

1ft=12inches

So, T=115F=115+459.67=574.67R

$Psia=\frac{lbf}{in^2}=\frac{lbf}{(\frac{1}{12})^2ft^2}$

By ideal gas equation

PV=mrt

$\frac{70}{ (\frac{1}{12})^2}( \frac{lbf}{ft^2})\times \frac {3π}{4}D^3(ft^3)=15(lbm)\times45(\frac{lbf-ft}{lbm°R})\times 574.67°R$

Unit of bath side is balanced

Diametr D=2.537 ft

Height $H=3\times D=3\times 2.537$

H=7.6115ft