A sealed container with negligible co-efficient of...

A sealed container with negligible co-efficient of volumetric expansion contains helium (a monatomic gas) when it is heated from $200 \mathrm{~K}$ to $400 \mathrm{~K}$, the average $\mathrm{K} . \mathrm{E}$. of helium atom is (A) Halved (B) Doubled (C) Unchanged (D) Increased by factor $\sqrt{2}$

A sealed container with negligible co-efficient of volumetric expansion contains helium (a monatomic gas) when it is heated from $200 \mathrm{~K}$ to $400 \mathrm{~K}$, the average $\mathrm{K} . \mathrm{E}$. of helium atom is
(A) Halved
(B) Doubled
(C) Unchanged
(D) Increased by factor $\sqrt{2}$

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Key Concepts

Absolute Temperature

Absolute temperature, measured in Kelvin, is a fundamental thermodynamic property that directly influences the kinetic energy of gas particles. In the kinetic theory of gases, as the absolute temperature increases, the average kinetic energy of the gas molecules increases proportionally.

Equipartition Theorem

The equipartition theorem in statistical mechanics states that energy is shared equally among all available degrees of freedom. For a monatomic ideal gas, this means that every helium atom has an average kinetic energy directly proportional to the absolute temperature, with the relationship given as (3/2)kT, where k is Boltzmann's constant.

Kinetic Energy of Gas Molecules

For monatomic gases like helium, the average kinetic energy of the molecules is precisely determined by the temperature, using the relation (3/2)kT. This shows that if the temperature is doubled, the average kinetic energy of each atom is also doubled, reflecting the linear dependence of kinetic energy on temperature.

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