$A$ diatomic gas of molecular weight $30 \, g/mol$ is filled in a container at $27 \, ^\circ C$. It is moving at a velocity of $100 \, m/s$. If it is suddenly stopped,the rise in temperature of the gas is:

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement-$1$: The internal energy of a perfect gas is entirely kinetic and depends only on the absolute temperature of the gas and not on its pressure or volume.
Statement-$2$: $A$ perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat,the temperature rise of the gas at constant pressure is lower than that at constant volume.

Given below are two statements:
Statement $I$: The temperature of a gas is $-73^{\circ} C$. When the gas is heated to $527^{\circ} C$,the root mean square speed of the molecules is doubled.
Statement $II$: The product of pressure and volume of an ideal gas is equal to the translational kinetic energy of the molecules.
In the light of the above statements,choose the correct answer from the options given below:

The density of water is $1000 \; kg \; m^{-3}$. The density of water vapour at $100 \; ^{\circ}C$ and $1 \; atm$ pressure is $0.6 \; kg \; m^{-3}$. The volume of a molecule multiplied by the total number gives what is called molecular volume. Estimate the ratio (or fraction) of the molecular volume to the total volume occupied by the water vapour under the above conditions of temperature and pressure.

Speed of sound in a gas is $v$ and $r.m.s.$ velocity of the gas molecules is $c.$ The ratio of $v$ to $c$ is

$A$ balloon carries a total load of $185\; \text{kg}$ at normal pressure and temperature of $27^{\circ} \text{C}$. What load will the balloon carry on rising to a height at which the barometric pressure is $45\; \text{cm}$ of $\text{Hg}$ and the temperature is $-7^{\circ} \text{C}$? Assume the volume is constant. (in $\text{kg}$)