Kinetic Interpretation of Temperature and RMS Speed of Gas Molecules

Kinetic Interpretation of Temperature – The molecules in solids are bonded together such that the molecules cannot move around freely but they do vibrate, and these vibrations are random, particle exerts a force on each other, and thus they attain kinetic energy due to motion and potential energy due to the interaction.

Kinetic Interpretation of Temperature

The temperature of a body is the measure of the average kinetic energy of a body.

Temperature in Kelvin = Temperature in degree Celsius + 273

As absolute zero is equal to 0 in the Kelvin scale, it is also known as the absolute scale.

In a gas the particles are always in a state of random motion, all the particles move at different speed constantly colliding and changing their speed and direction,

RMS Speed of Gas Molecules

RMS or Root Mean Square method, squaring the velocity and then taking a square root we can overcome the “direction” component of velocity and still get the average velocity. Since we have removed the direction component, it is no longer average velocity, rather we can call it average speed, and the equation for RMS speed is given as follows,

\( v_{rms} \) = \( \sqrt{\frac{3RT}{M}} \)

Where v_rmsis the root-mean-square velocity, M is the molar mass of the gas (Kg/mole), R is the molar gas constant, and T is the temperature in Kelvin.

We can see that v_rms reduce as the temperature approaches absolute zero.

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