What does Boyle's Law prove quantitatively? Why?

What will be the value of the gas constant $R$ when pressure is expressed in $dyne \, m^{-2}$ and volume in $mm^3$?

The use of hot air balloons for sports and meteorological observations is based on which of the following laws?

$A$ gas has a volume of $3.4 \ L$ at $25^{\circ} C$. What is the final temperature if the volume increases to $10.2 \ L$ at constant pressure (in $K$)?

Find the pressure of a $CO_2$ gas when $6.022 \times 10^{22}$ molecules are placed in a $2 \ L$ vessel at $27 \ ^oC$ temperature. (in $bar$)

If the density of a gas at sea level is $1.5 \ mg \ L^{-1}$,find the density of that gas on Mount Abu,where the pressure is $0.5 \ bar$. (Assume pressure at sea level is $1.0 \ bar$ and use the formula $\frac{d_1}{d_2} = \frac{p_1}{p_2}$) (in $mg \ L^{-1}$)