Question

The pressure of an ideal gas is written as $P={\displaystyle \frac{2E}{3V}}.$ Here $E$ stands for
A. total translational kinetic energy
B. rotational kinetic energy
C. average translational kinetic energy
D. total kinetic energy

Answer 1

Hint We know that an ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces. One can visualize it as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other. In most usual conditions (for instance at standard temperature and pressure), most real gases behave qualitatively like an ideal gas. Many gases such as nitrogen, oxygen, hydrogen, noble gases, and some heavier gases like carbon dioxide can be treated like ideal gases within reasonable tolerances.

Complete step by step answer
 Given in the question that,
 $\mathrm{P}={\displaystyle \frac{2\mathrm{E}}{3\mathrm{V}}}$
$\Rightarrow \mathrm{PV}={\displaystyle \frac{2}{3}}\mathrm{E}$
$\Rightarrow \mathrm{nRT}={\displaystyle \frac{2}{3}}\mathrm{E}\{$ as $\mathrm{PV}=\mathrm{nRT}$ ideal gas equation $\}$
$\Rightarrow {\displaystyle \frac{3}{2}}\mathrm{nRT}=\mathrm{E}$
$\Rightarrow {\displaystyle \frac{3}{2}}\mathrm{KT}=\mathrm{E}\{\mathrm{K}=\mathrm{nR}\}$
According to the law of equipartition of energy it has 3 degrees of freedom and thus it is translational kinetic energy. Hence, the answer is total translational kinetic energy.

Therefore, the correct answer is Option A.

Note: We can conclude that the model, called the kinetic theory of gases, assumes that the molecules are very small relative to the distance between molecules. The molecules are in constant, random motion and frequently collide with each other and with the walls of any container. The higher the temperature, the greater the motion. The kinetic theory of gases explains the macroscopic properties of gases, such as volume, pressure, and temperature, as well as transport properties such as viscosity, thermal conductivity and mass diffusivity. The model also accounts for related phenomena, such as Brownian motion. The kinetic molecular theory can be used to explain each of the experimentally determined gas laws. The pressure of a gas results from collisions between the gas particles and the walls of the container. Each time a gas particle hits the wall, it exerts a force on the wall.