Consider a container filled with ideal gas and is covered by a frictionless and lightweight piston that exerts pressure on the gas.
I understand that during an isobaric process, the container is in contact with a pressure reservoir, ensuring that the gas is in mechanical equilibrium with its surroundings for the whole process. This process happens quasistatically.
I am uncertain how this process works step-by-step. Suppose a small amount of heat is added to the container, it causes the gas to have greater pressure than its surroundings (in quasistatic process, the pressure of the gas is infinitesimally greater than its surroundings so that $\Delta P$ is negligible which makes pressure constant). In order to respond to this pressure imbalance, the gas expands until mechanical equilibrium is reached. According to the ideal gas law $P\Delta V=nR\Delta T$, volume increase causes the temperature to increase. Did I understand it correctly?
Also there is one thing that bothers me: If gas expands, then it performs work on the surroundings right? In that case, its internal energy should decrease which in turn decreases temperature, according to this formula $\Delta U=\frac{f}{2}Nk_B\Delta T$, no? I am not sure why temperature increases during an isobaric process.
Best Answer
Maintaining a constant external pressure does not ensure that the gas is in mechanical equilibrium with its surroundings for the whole process. Carrying out the process quasi statically and without friction ensures it.
You've got it backwards. The temperature increase causes the volume to increase, with the ratio of temperature to volume being constant for a constant pressure process.
Correct.
The internal energy does not decrease, it increases. That's because, for a constant pressure process, part of the energy transfer to the gas by heat performs work while part increases its temperature (and thus internal energy). From the first law $$Q=\Delta U+W$$
The key to the process is keeping the external pressure constant. For an example, see the Figure below where the piston/cylinder is vertically oriented and a weight is placed on top of the piston.
Ignoring the mass of the piston, the total external pressure is as shown. It is fixed. The piston/cylinder is placed in a thermal bath or reservoir of constant temperature infinitesimally greater than the gas temperature. This results in an infinitesimal transfer of heat to the gas increasing the gas temperature and pressure and doing an infinitesimal amount of work raising the weight. The gas then comes into thermal equilibrium and mechanical equilibrium with surroundings. The process is repeated with additional higher temperature thermal reservoirs continually taking in heat, increasing temperature, and performing work, always coming into equilibrium with the same constant external pressure.
Hope this helps.