Understanding Isothermal Processes

[bjgawp]

I've gone through a some of our textbooks but none of them effectively explains this process clearly. For the isothermal process, according to the first law of thermodynamics, ΔU = 0, indicating that Q = -W. So if heat flows into the system, all the energy put in is converted to work which the gas does on the surroundings. However, microscopically, how do the molecules exert more force on the wall (i.e. more pressure) without a change in their kinetic energy (i.e. their internal energy)? Taking a container with a movable piston, if the gas moves the piston by work - doesn't that mean that the molecules have gained more kinetic energy to move it?

Thanks in advance!

 

[lpfr]

Yes, when you heat the gas the molecules gain kinetic energy, and they lose it pushing the piston.

 

[m2003]

I can provide a response to your question regarding isothermal processes. First, let's define what an isothermal process is. It is a thermodynamic process where the temperature of a system remains constant throughout the process. This means that the internal energy of the system remains unchanged, as you have correctly stated. In this case, the first law of thermodynamics tells us that the change in internal energy (ΔU) is equal to the heat flow (Q) into the system minus the work (W) done by the system. In an isothermal process, since ΔU = 0, this means that Q = -W.

Now, let's address your question about how the molecules exert more force on the wall (increased pressure) without a change in their kinetic energy. This can be explained by looking at the microscopic level of the gas molecules. In an isothermal process, the temperature remains constant, but this does not mean that the individual molecules do not have different velocities (kinetic energies). Some molecules may have higher velocities while others may have lower velocities, but on average, the temperature remains constant. So, when the gas molecules collide with the walls of the container, they transfer their momentum to the walls, resulting in an increase in pressure. This does not necessarily mean that all the molecules have gained more kinetic energy, but rather that the overall average kinetic energy remains constant.

In the case of a movable piston, the work done by the gas on the piston is due to the transfer of kinetic energy from the gas molecules to the piston. This transfer of energy is a result of the collisions between the gas molecules and the piston. So, in this scenario, the molecules are not gaining more kinetic energy, but rather transferring their existing kinetic energy to the piston to do work.

I hope this explanation helps to clarify your understanding of isothermal processes. It is important to remember that at the microscopic level, there is a constant exchange of energy between the gas molecules and their surroundings, but at the macroscopic level, the temperature remains constant. This is what makes isothermal processes unique and important in thermodynamics.