Question

A spherical tank is being designed to hold 10 moles of carbon dioxide gas at an absolute pressure of 5 bar and a temperature of 80°F. What diameter spherical tank should be used? The molecular weight of methane is 44 g/mole.

Answer 1

Answer:

r=0.228m

Explanation:

The equation that defines the states of a gas according to its thermodynamic properties is given by the general equation of ideal gases

PV=nRT

where

P=pressure =5bar=500.000Pa

V=volume

n=moles=10

R = universal constant for ideal gases = 8.31J / (K.mol)

T=temperature=80F=299.8K

solvig For V

V=(nRT)/P

$V=(\frac{(10)(8.31)(299.8)}{500000} )\\V=0.0498m^3$

we know that the volume of a sphere is

$V=\frac{4\pi r^3}{3}$

solving for r

$r=\sqrt[3]{ \frac{3 V}{4\pi } }$

solving

$r=\sqrt[3]{ \frac{3 (0.049)}{4\pi } }\\r=0.228m$