Question

The pressure exerted by gas is P.If the mass of molecule becomes half and velocity becomes double then pressure will become

Answer 1

Answer on Question #44263-Physics-Molecular Physics-Thermodynamics

The pressure exerted by gas is P. If the mass of molecule becomes half and velocity becomes double then pressure will become

Solution

The equation of state is

$$P = n k T,$$

where $k$ is the Boltzmann's constant, $n$ is the concentration of molecules, $T$ is temperature.

We know that

$$T \sim \frac{m v^2}{2}.$$

So

$$P \sim m v^2.$$

If the mass of molecule becomes half and velocity becomes double then pressure will become

$$P' = P \frac{\left(\frac{m}{2}\right) (2 v)^2}{m v^2} = P \frac{\left(\frac{m}{2}\right) 4 v^2}{m v^2} = 2 P.$$

Answer: $2P$.

https://www.AssignmentExpert.com