The molar heat capacity of oxygen gas at STP is nearly 2.5R....

The molar heat capacity of oxygen gas at STP is nearly 2.5R. As the temperature is increased, it gradually increases and approaches $3.5 R$. The most appropriate reason for this behaviour is that at high temperature: (a) oxygen does not behave as an ideal gas (b) oxygen molecules dissociate in atoms (c) the molecules collide more frequently (d) molecular vibrations gradually become effective

The molar heat capacity of oxygen gas at STP is nearly 2.5R. As the temperature is increased, it gradually increases and approaches $3.5 R$. The most appropriate reason for this behaviour is that at high temperature:
(a) oxygen does not behave as an ideal gas
(b) oxygen molecules dissociate in atoms
(c) the molecules collide more frequently
(d) molecular vibrations gradually become effective

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Key Concepts

Degrees of Freedom

Molecules have various degrees of freedom—translational, rotational, and vibrational—that contribute to their internal energy and, consequently, their heat capacity. In a diatomic molecule such as oxygen, at lower temperatures only translational and rotational motions contribute significantly, while vibrational modes remain largely inactive.

Equipartition Theorem

The equipartition theorem in statistical mechanics states that each quadratic degree of freedom contributes an equal amount of energy to the system's overall internal energy. As temperature increases, additional degrees of freedom, particularly vibrational modes, begin to contribute, incrementally raising the molar heat capacity.

Vibrational Modes

At higher temperatures, the vibrational motion of molecules—which involves both kinetic and potential energy components—becomes increasingly activated. This gradual activation of vibrational modes in diatomic molecules like oxygen results in added energy contributions that elevate the molar heat capacity towards the higher value observed.

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