Which of the following laws is followed by a hot air balloon used for sports and meteorology?

The value of the universal gas constant $R$ is the same for all gases. What is its physical significance?

The pressure exerted by a non-reactive gaseous mixture of $6.4 \ g$ of methane and $8.8 \ g$ of carbon dioxide in a $10 \ L$ vessel at $27^{\circ} C$ is .............$kPa$.
(Round off to the Nearest Integer).
[Assume gases are ideal,$R = 8.314 \ J \ mol^{-1} K^{-1}$
Atomic masses $: C = 12.0 \ u, H = 1.0 \ u, O = 16.0 \ u]$

$A$ gas at a pressure of $2 \ atm$ is heated from $25^{\circ} C$ to $323^{\circ} C$ and simultaneously compressed to $\frac{2}{3}$ of its original volume. What is the final pressure (in $atm$)?

How many moles of $He$ gas occupy $22.4 \, L$ at $30^{\circ}C$ and $1 \, atm$ pressure?

Derive the relation between the density of gases and their molecular mass using Avogadro's law.