Question

The parameter that remains the same for molecules of all gases at a given temperature is :

• A. kinetic energy
• B. momentum
• C. mass
• D. speed

Answer 1

The Correct Option is A

To identify the constant parameter for molecules of all gases at a specific temperature, understanding the relationship between gas temperature and the kinetic theory of gases is essential.

The kinetic theory of gases models a gas as a vast quantity of minute particles (atoms or molecules) in perpetual, random motion. A core assumption of this theory is that a gas's temperature is directly proportional to the average kinetic energy of its constituent molecules.

1. Kinetic Energy: Per the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to the gas's absolute temperature. This relationship is mathematically represented as: \(E_k = \frac{3}{2}kT\), where \(E_k\) denotes average kinetic energy, \(k\) is the Boltzmann constant, and \(T\) signifies absolute temperature. Consequently, at any given temperature, the average kinetic energy is uniform across molecules of all gases.
2. Momentum: A molecule's momentum is calculated as the product of its mass and velocity (\((p = mv)\)). As the masses and velocities of gas molecules vary, momentum is not constant across different gases at a uniform temperature.
3. Mass: The mass of a molecule is intrinsically linked to its gas type. Different gases possess distinct molecular masses. Therefore, mass does not remain constant for molecules of all gases.
4. Speed: The speed of gas molecules is contingent upon their kinetic energy and mass. Given that different gases have varying masses, molecular speed will differ even when kinetic energy is identical.

In summary, from the parameters examined, kinetic energy is the one that remains constant for molecules of all gases at a given temperature. This aligns with the principle that temperature serves as a metric for the average kinetic energy of gas molecules.