If the mass of each molecule of a gas kept at a constant pressure $P$ in a container is halved and their speed is doubled,what will be the resulting pressure of the gas?

An ideal gas in a container of volume $500 \text{ c.c.}$ is at a pressure of $2 \times 10^5 \text{ N/m}^2$. The average kinetic energy of each molecule is $6 \times 10^{-21} \text{ J}$. The number of gas molecules in the container is:

The $rms$ speed of an ideal hydrogen gas molecule in a gas chamber at $0^{\circ}C$ is $3180 \ m/s$. What is the pressure of the hydrogen gas in atmospheres? (Given: Density of hydrogen gas $\rho = 8.99 \times 10^{-2} \ kg/m^3$,$1 \ atm = 1.01 \times 10^5 \ N/m^2$)

What is the kinetic energy of $1$ mole of a monatomic gas?

Internal energy of an ideal gas depends on which factors and does not depend on which factors?

Consider a rectangular block of wood moving with a velocity $v_{0}$ in a gas at temperature $T$ and mass density $\rho$. Assume the velocity is along the x-axis and the area of cross-section of the block perpendicular to $v_{0}$ is $A$. Show that the drag force on the block is $4\rho A v_{0} \sqrt{\frac{kT}{m}}$,where $m$ is the mass of the gas molecule.