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

It’s the same case with liquids and gases instead of vibrating they move randomly, now the speed at which they move increases with temperature, cooling down will make them move slowly, therefore,

Kinetic Interpretation of Temperature

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

We should note that temperature of a body always depends upon its average kinetic energy and since the average kinetic energy can have a minimum possible value of zero, therefore an object cannot be cooled below a certain minimum value, this value is known as absolute zero. This is the lowest possible temperature in our universe and no object could be cooled to this temperature, it is equivalent to -273 degree Celsius or 0 Kelvin. These two scales of temperature can be converted with the following expression,

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,

Kinetic Interpretation of Temperature

As the particles collide and change velocity it is not practical to measure each velocity, and as there are particles moving in one direction equal to the particles moving in the opposite direction they cancel out and the average velocity will be equal to zero, hence there is an alternate way to determine their average velocity.

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 vrmsis 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 vrms reduce as the temperature approaches absolute zero.

The rms speed takes both molecular weight and temperature into account, which are the factors that directly affect the kinetic energy of a gas.

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Practise This Question

Figure shows a vertical cylindrical vessel separated in two parts by a frictionless piston free to move along the length of the vessel. The length of the cylinder is 90 cm and the piston divides the cylinder in the ratio of 5:4. Each of the two parts of the vessel contains 0.1 mole of an ideal gas. The temperature of the gas is 300 K in each part. Calculate the mass of the piston