Why doesn't a temperature and pressure gradient exist in a container of real gas?

In the Kinetic theory of gases, it is assumed that there are no intermolecular forces between the atoms/molecules. But real gases, have intermolecular attractive and repulsive forces.

Suppose a container filled with a real gas.

The molecules well inside that container will feel no net force of attraction/repulsion on any side. But considering molecules near the boundaries of the container, a net inward force will be felt. I think this will make velocities of atoms less than that of the atoms well inside the container.

So, is the pressure at the centre of the container more than that of the pressure at the boundary(measured actual pressure)?

My book says that the slowing down does not mean that the gas is cooler close to the walls. The relation of $\sqrt{T} \propto v_{\mathrm{rms}}$ is valid only in the absence of intermolecular forces. Temperature is defined by the Zeroth Law. Will net energy/heat transfer take place between the atoms of the gas and the metal bar if I keep a metal of temperature $T$ inside the container near the boundary? Here, $T$ is the temperature at the centre of the container such the no heat transfer takes place if a metal bar is kept at temperature $T$ at the centre of the container.

• Most gases under normal conditions are closer to ideal than van der waals states. The extra terms in the VDW equation account for the non-ideal behaviour when they are close to liquefaction and are insignificant under normal conditions. – matt_black Jul 27 '17 at 17:15
• Most "containers" are "small," so temperature and pressure variations are insignificant. But think of the earth's atmosphere. Temperature and pressure variations are significant in the atmosphere. The sun is essentially a ball of gas. Look at what happens there... – MaxW Jul 27 '17 at 17:36