Question

We have a Carnot cycle and lets say it is in thermal and mechanical equilibrium with the surroundings before the beginning of the process. I am using the convention that heat brought to the system is positive and the work done by the system is positive.

After the isothermal expansion has happened, isentropic expansion starts. The ideal gas does some more work, in turn cooling itself. The question is why this happens? What forces the gas to to some more work during the isentropic expansion?

Answer 1

During isothermal expansion, an ideal gas does work while absorbing heat to maintain temperature with no change in internal energy. In the subsequent adiabatic expansion, the gas does work derived from its internal energy, leading to a decrease in temperature as it is thermally insulated.

Step-by-step explanation:

The question addresses why an ideal gas continues to do work during isentropic expansion in a Carnot cycle. During the isothermal expansion phase, the gas absorbs heat Qin to maintain its temperature while doing work W1. The internal energy change (ΔEint) is zero because the internal energy of an ideal gas depends solely on temperature.

As the process transitions to an adiabatic expansion, no heat is added or removed from the system (Q = 0), and the work W2 done by the gas must come from its internal energy. This results in cooling the gas from a higher temperature (Th) to a lower temperature (Tc). The driving force for the gas to do work during this adiabatic expansion is the imbalance of forces as weights on the piston are removed, causing the piston to move and the gas to expand and cool due to the work done on the surroundings.