$0.056 \, kg$ of Nitrogen is enclosed in a vessel at a temperature of $127 \, ^{\circ}C$. The amount of heat required to double the speed of its molecules is $k \, cal$. (Take $R = 2 \, cal \, mole^{-1} K^{-1}$)

What is/are the same for $O_2$ and $NH_3$ in gaseous state?

$Assertion :$ Air pressure in a car tyre increases during driving.
$Reason :$ Absolute zero temperature is not zero energy temperature.

The number density of molecules of a gas depends on their distance $r$ from the origin as $n(r) = n_0 e^{-\alpha r^4}$. Then the total number of molecules is proportional to

The adiabatic elasticity of hydrogen gas $(\gamma = 1.4)$ at $NTP$ 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.