Statement-1: Internal energy of a gas U = nC_ | vedclass

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(B) Statement-$1$ is True. The internal energy $U$ of an ideal gas is defined as the sum of the kinetic energies of its molecules due to their random

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Statement-$1$ is True,Statement-$2$ is True; Statement-$2$ is not a correct explanation for Statement-$1$.

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(B) Statement-$1$ is True. The internal energy $U$ of an ideal gas is defined as the sum of the kinetic energies of its molecules due to their random translational,rotational,and vibrational motions. For an ideal gas,$U = nC_VT$.Statement-$2$ is True. When the container is suddenly stopped,the macroscopic kinetic energy of the gas (due to the motion of the container) is converted into the microscopic kinetic energy of the gas molecules through collisions. This increase in microscopic kinetic energy results in an increase in the temperature of the gas.However,Statement-$2$ describes a process of energy conversion (mechanical to thermal) and does not explain why internal energy is defined as $U = nC_VT$. Therefore,Statement-$2$ is not the correct explanation for Statement-$1$.

Column $- I$	Column $- II$
$(A)$ Root mean square speed of gas molecules	$(P)$ $\frac{1}{3} n m \bar{v}^{2}$
$(B)$ Pressure exerted by ideal gas	$(Q)$ $\sqrt{\frac{3 RT}{M}}$
$(C)$ Average kinetic energy of a molecule	$(R)$ $\frac{5}{2} RT$
$(D)$ Total internal energy of $1$ mole of a diatomic gas	$(S)$ $\frac{3}{2} k_{B} T$

Statement-$1$: Internal energy of a gas $U = nC_VT$ is due to the random motion of gas molecules.
Statement-$2$: $A$ container is moving with speed $v$. It is suddenly stopped by a force,and the temperature of the gas increases.

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Statement-$1$: Internal energy of a gas $U = nC_VT$ is due to the random motion of gas molecules.Statement-$2$: $A$ container is moving with speed $v$. It is suddenly stopped by a force,and the temperature of the gas increases.