Work is being done on the the atoms in the wall, in contact with the
hands, when we push (hard) on the wall.
At the macroscopic level the wall is considered a rigid body, and since the wall as a whole is not displaced, no work is done.
On the microscopic level you are doing work pushing on the wall by displacing layers of atoms in the wall (but mostly displaces the atoms of your hand). This in effect is stored as strain energy which, after you remove the force, is responsible for moving the atoms back to their original configuration.
When we push the wall, energy is being transferred as heat energy (due
to friction between hand and wall) which increases the kinetic energy
of the atomic particles on the wall, thus increasing the temperature
of the area in contact.
Heat is energy transfer due solely to temperature difference. Any energy transfer by heat to the wall would be due to the temperature of our hand being greater than the wall.
An increase in temperature due to friction is actually energy transfer by friction work, not by heat. If you rub your hands together on a cold day to keep warm, you are doing friction work. It is the friction work that increases the temperature of your hands skin. In any event, simply pushing on a wall does not involve kinetic friction unless you rub your hands against the wall.
In any event, simply pushing on a wall does ..... the wall." Had I
assumed that there is some frictional force between the hand and wall,
which leads to increase in temperature of wall compared to initial
condition, would it then be heat (transfer of thermal energy) or work
done by friction (increase in the mechanical energy of the atoms in
the wall in contact) or both?
It would be work transfer, not heat transfer. Consider compressing a gas. When you compress a gas its temperature rises. The temperature rise is not due to heat (energy transfer due to temperature difference) but due to work (force times displacement).
Now once the friction work increases the temperature of the surface of the wall (as well as your hand), it can be followed by heat transfer from the surface of the wall to the interior of the wall because the wall surface temperature is higher than the interior temperature.
That leads me to another question : doesn't heat increases the
mechanical energy(KE+PE) of the atoms/molecules too? Which would mean
that heat is also a type work. Please correct me where I am wrong?
Yes, heat transfer can increase the KE and PE of the atoms/molecules of a substance (though we primarily consider it with respect to KE unless a material undergoes a phase change). But the mechanism is not the same as work. The mechanism is energy transfer due solely to temperature difference. Work is not energy transfer due to temperature difference. It is due to force times displacement.
That said, heat transfer can result in work and work transfer can result in heat.
If I expose a gas in a cylinder fitted with a piston to a body at a higher temperature than the gas, there will be heat transfer from that body to the gas increasing its temperature. The increase in temperature of the gas causes it to expand against the piston resulting in the gas doing work on its surroundings.
Likewise, if I compress the gas the work I do transfers energy to the gas increasing its temperature. Then you can have energy transfer from the gas to lower temperature surroundings by means of heat.
Hope this helps.
