Question

I am self-studying thermodynamics, and was reading up Carnot heat engine (Yunus Cengel - thermodynamics book). So, the experiment in the textbook is set up such that, we have an adiabatic piston-cylinder device and the insulation at the cylinder head can be removed to transfer energy from thermal energy reservoir(s) to supply/absorb heat depending upon the where you are in the cycle. It begins with reversible isothermal process by connecting the cylinder to a heat source at temperature T_H. The gas expands, which is also at temperature T_h, and does work on the piston and temperature of the gas drops. This where I have some doubts.

Now, why does the gas expand if both the hot reservoir and system is in thermal equilibrium (same temp. T_h)?. Secondly, from the ideal gas equation Pv = RT, isn't volume and temperature proportional to each other, i.e., as the volume of the gas increases, shouldn't the temperature increase as well?
Options:
A) The expansion occurs due to the difference in pressures between the gas and the surroundings.
B) The gas expands spontaneously due to an internal energy change despite the thermal equilibrium.
C) The ideal gas law demonstrates the inverse relationship between volume and temperature.
D) The gas expansion happens via an increase in temperature caused by an external energy source.

Answer 1

In a Carnot heat engine, the gas expands during the isothermal process because it does work on the piston, resulting in a pressure decrease while temperature remains constant due to the thermal equilibrium with the heat reservoir. The ideal gas law explains this behavior since, at constant temperature, the volume increase leads to a pressure decrease to keep PV = nRT balanced.

Step-by-step explanation:

The expansion of the gas in the Carnot heat engine during the isothermal process occurs even though the gas and the hot reservoir are at the same temperature (Th) because the gas does work on the piston. The ideal gas law indicates that, for a constant temperature, as the volume (V) of the gas increases during an isothermal expansion, the pressure (P) must decrease to maintain the equation PV = nRT. The correct choice that explains the behavior of the gas during this phase is A) The expansion occurs due to the difference in pressures between the gas and the surroundings. The decrease in pressure is a result of the work done by the gas on the piston, and since the process is isothermal, the temperature remains constant despite the increasing volume.

During an adiabatic expansion, no heat enters or exits the system, and as the gas does work on the surroundings, the temperature drops since the internal energy decreases. The temperature decreases according to the relation TVY - 1 = constant, which reflects the adiabatic process for an ideal gas, where Y represents the specific heat ratio.