$A$ 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 $atm$)?

$A$ sample of gas occupies a volume of $0.2 \, L$ at $1 \, atm$ pressure and $0 \, ^oC$ temperature. What will be its volume in $L$ at the same pressure but at $273 \, ^oC$ temperature?

Explain: Gay-Lussac's Law.

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. $L_1$ and $L_2$ are the lengths of the gas columns before and after the expansion,respectively. The ratio $\frac{T_2}{T_1}$ is:

At $273 \ K$ temperature and $76 \ cm \ Hg$ pressure, the density of a gas is $1.964 \ g \ L^{-1}$. The gas is

Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load when a balloon of radius $10 \, m$,mass $100 \, kg$ is filled with helium at $1.66 \, bar$ at $27^{\circ} C$. (Density of air $= 1.2 \, kg \, m^{-3}$ and $R = 0.083 \, bar \, dm^{3} \, K^{-1} \, mol^{-1}$).