Correct Answer - Option 1 : increase in average molecular speed
CONCEPT:
- According to kinetic energy theory, if we increase the temperature of a gas, it will increase the average kinetic energy of the molecule, which will increase the motion of the molecules.
- This increased motion increases the outward pressure of the gas.
- The average kinetic energy of translation per molecules of the gas is related to temperature by the relationship:
\(⇒ KE = \frac{3}{2}{k_B}T\)
Where E = kinetic energy, kB = Boltzmann constant and T = temperature
EXPLANATION:
- The average kinetic energy of translation per molecules of the gas is related to temperature by the relationship:
\(⇒ KE = \frac{3}{2}{k_B}T\) -----(1)
- From the above equation, it is clear that the average kinetic energy of the gas molecule is directly proportional to the absolute temperature of the gas.
- So, if the temperature is increasing, the average velocity of the gas also increases.
According to the kinetic theory of gases, the relation between the pressure and the average velocity of the gas is given as,
\(⇒ P=\frac{Nmv^{2}}{3V}\) -----(2)
Where N = number of molecules, m = mass of the gas molecule, v2 = average velocity of the gas, and V = volume
Since volume is constant, so by equation 2,
⇒ P ∝ v2 -----(3)
- So when the temperature of the gas is increased its average velocity increases and by equation 3 it is clear that if the average velocity of the gas increases at constant volume, its pressure also increases.
- Hence, option 1 is correct.
