Question

The kinetic energy of molecules is directly proportional to:

• A. Temperature
• B. Pressure
• C. Both a and b

Answer 1

The correct option is A

Temperature

Explanation for the correct option:

1. Kinetic energy is the measure of average energy possessed by the molecules due to their motion and temperature.
2. From the kinetic interpretation of temperature, we know that:
   $\mathrm{E}=\frac{3}{2}\mathrm{nRT}$
3. Where, $\mathrm{E}=$ Kinetic Energy, $\mathrm{n}=$number of moles, $\mathrm{R}=$ Gas constant, $\mathrm{T}=$ temperature
4. Dividing both sides by $\mathrm{N}$, we get :$\frac{\mathrm{E}}{\mathrm{N}}=\frac{3}{2}{\mathrm{k}}_{\mathrm{B}}\mathrm{T}$
   Where,${\mathrm{k}}_{\mathrm{B}}=\frac{\mathrm{R}}{{\mathrm{N}}_{\mathrm{A}}}$, is the Boltzmann constant
5. Thus, the average kinetic energy is given as: $\mathrm{K}.\mathrm{E}=\frac{3}{2}{\mathrm{k}}_{\mathrm{B}}\mathrm{T}$
6. Hence, we can conclude that the average kinetic energy of the molecules is directly proportional to the temperature of the gas and is independent of pressure, volume, or the nature of the gas.
7. This fundamental result relates the gas's temperature to the average kinetic energy of a molecule.

Hence, option A is correct.