The relationship between translational kinetic energy of the molecules in a gas 'E' and its temperature 'T' is ________.

CONCEPT:

• The pressure in a gas developed due to the collisions between the gaseous molecules.
• Kinetic energy: The energy possessed by the molecule of the gas due to its motion is called kinetic energy of the gas molecules.
  • ​It is denoted by E or KE.

The kinetic energy of gas molecules is given by:

\(Kinetic\;energy\;of\;gas\;molecules\;\left( {E} \right) = \frac{{3N\;K_B\;T}}{2}\)

Where K is Boltzmann constant, T is temperature and N is the number of molecules.

EXPLANATION:

The translational kinetic energy of the molecules is given by:

\(Kinetic\;energy\;of\;gas\;molecules\;\left( {E} \right) = \frac{{3N\;K_B\;T}}{2}\)

⇒2 E = 3 K_B N T

So option 2 is correct.

EXTRA POINTS:

The pressure exerted by a gas:

• According to kinetic theory, the molecules of a gas are in a state of continuous random motion.
• They collide with one another and also with the walls of the vessel.
• Whenever a molecule collides with the wall, it returns with a changed momentum, and an equal momentum is transferred to the wall (conservation of momentum).
• According to Newton's second law of motion, the rate of transfer of momentum to the wall is equal to the force exerted on the wall.
• Since a large number of molecules collide with the wall, a steady force is exerted on the wall.
• The force exerted per unit area of the wall is the pressure of the gas.
• Hence a gas exerts pressure due to the continuous collisions of its molecules with the walls of the vessel.