$[20$ points$]$

$3.)$ A spherical ballon is filled with helium gas at $20$degC. Investigate the effect of the ballon diameter on the mass of helium contained in a spherical ballon for the pressures $($P$)$ of $($a$)100$ kPa and $($b$)200$ kPa $.$ Let the diameter vary from $5$ m to $15$ m in steps of $1$ m $.$ Plot the mass of helium against the diameter for both the cases. Comment on the plot. Keep the units of all the parameters in SI$.$

To compute mass $(m)$ of the helium gas in the ballon, you may use the following equation based on the ideal gas law:

In the above equation:

$m=\frac{PV}{R_{He}T}$

$m=$ Mass of the helium gas in kg $.$

$P=$ Pressure of helium gas in the ballon in Pa

$V=$ Volume of the spherical ballon in $m^3$

$R_{He}=$ Specific gas constant for helium $=2077\frac{J}{k}g.K$

$T=$ Temperature in K

$($Done in Excel$)$