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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

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

Vedclass · Answer

(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-$1$.

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.

Similar Questions

According to the kinetic theory of gases,which one of the following statements is wrong?

An ideal gas of molar mass $M$ is contained in a very tall vertical cylindrical column in a uniform gravitational field. Assuming the gas temperature to be $T$, the height at which the centre of gravity of the gas is located is (where $R$ is the universal gas constant).

Air inside a closed container is saturated with water vapour. The air pressure is $p$ and the saturated vapour pressure of water is $\bar{p}$. If the mixture is compressed to one half of its volume by maintaining temperature constant, the pressure becomes

$A$ rocket is propelled by a gas which is initially at a temperature of $4000\, K$. The temperature of the gas falls to $1000\, K$ as it leaves the exhaust nozzle. The gas which will acquire the largest momentum while leaving the nozzle is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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.