Final Answer:
The root mean square velocity of an ideal gas at constant pressure varies with density (d) as 1/√d. Option D is answer.
Step-by-step explanation:
The root mean square velocity (u_rms) of an ideal gas is defined as the square root of the average of the squares of the velocities of all the gas molecules. It is given by the formula:
u_rms = √(3kT/M)
where k is Boltzmann's constant, T is the temperature in Kelvin, and M is the molar mass of the gas.
At constant pressure, the temperature of an ideal gas is inversely proportional to its density. This can be expressed by the formula:
T = 1/(ρd)
where ρ is the density of the gas.
Substituting this expression for T into the formula for u_rms, we get:
u_rms = √(3k/(ρdM))
Taking the square root of both sides, we get:
u_rms ∝ 1/√d
Therefore, the root mean square velocity of an ideal gas at constant pressure varies with density (d) as 1/√d. Option D is answer.