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

r=0.228m

Step-by-step 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=(((10)(8.31)(299.8))/(500000) )\\V=0.0498m^3`

we know that the volume of a sphere is

`V=(4\pi r^3)/(3) \\`

solving for r

`r=\sqrt[3]{ (3 V)/(4\pi ) }`

solving

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