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

An evacuated glass vessel weighs $40.0 \ g$ when empty,$135.0 \ g$ when filled with a liquid of density $0.95 \ g \ mL^{-1}$ and $40.5 \ g$ when filled with an ideal gas at $0.82 \ atm$ at $250 \ K$. The molar mass of the gas in $g \ mol^{-1}$ is .... .
(Given : $R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1}$ )

What is called an ideal gas? Why?

$A$ steel cylinder contains helium gas at $250 \, kPa$ pressure and $300 \, K$ temperature. The cylinder can withstand a maximum pressure of $1 \times 10^6 \, Pa$. The room in which the cylinder is placed catches fire. Predict whether the cylinder will burst before it melts. (Melting point of the cylinder = $1800 \, K$)

During a reversible adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $\frac{C_p}{C_V}$ for the gas is:

If $P$,$V$,and $T$ represent pressure,volume,and temperature of the gas,the correct representation of Boyle's law is: