Question

What is kinetic interpretation of temperature? Derive relation between kinetic energy and temperature.
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Answer 1

answer:-

According to this relation average kinetic energy of a molecule of an ideal gas is proportional to its absolute temperature; is indeppendent of the pressure, volume or the nature of the ideal gas. This is called kinetic interpretation of temperature.

As stated in the kinetic-molecular theory, the temperature of a substance is related to the average kinetic energy of the particles of that substance. When a substance is heated, some of the absorbed energy is stored within the particles, while some of the energy increases the motion of the particles.

Answer 2

Answer:

According to this relationship, the average kinetic energy of a molecule in an ideal gas is independent of the ideal gas's pressure, volume, or composition and is proportional to its absolute temperature. Kinetic interpretation of temperature is what this is.

Explanation:

The kinetic interpretation of temperature is based on the fact that temperature is related to the average kinetic energy of the particles in a substance.

According to this interpretation, the temperature is a measure of the random motion of particles in a substance. The higher the temperature, the faster the particles are moving on average.

The relation between kinetic energy and temperature can be derived using the formula for the average kinetic energy of a particle in a gas:

$K.E. = \frac{1}{2} mv^{2}$

where KE is the kinetic energy, m is the mass of the particle, and v is the velocity of the particle.

The following equation relates the average kinetic energy of a gas's particles to its temperature:

$K.E . = \frac{3}{2} kT$

where k is the Boltzmann constant and T is the temperature in Kelvin.

The derivation of this equation is based on the assumptions of the kinetic theory of gases, which states that gas molecules are in constant random motion and that the temperature of a gas is related to the average kinetic energy of its molecules.

By equating the two equations for kinetic energy, we get:

$\frac{3}{2} kT = \frac{1}{2} mv^{2}$

Simplifying, we get:

$v^{2} =\frac{3kT}{m}$

$v =\sqrt{\frac{3kT}{m} }$

This equation shows that the velocity of gas particles is directly proportional to the square root of the temperature. Thus, as the temperature of a gas increases, the average velocity of its particles also increases, leading to an increase in kinetic energy.

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