# Carnot cycle modelization

In some sources, there's a slight difference in the Carnot cycle stages description. Let's take the "first" - the isothermal expansion.

Some say that as a consequence of the contact between the system and the hot reservoir, the system volume simply increases.

Some others (e.g. Chan, Al-Ghoul - Chemical thermodynamics) say the volume increase is due to a pressure lowering of the system.

Are those two diffent illustrations of the same concept? Why do we need to reduce the pressure (e.g. lowering the piston weight)?

Both statements are equivalent.

In some sources, there's a slight difference in the Carnot cycle stages description. Let's take the "first" - the isothermal expansion. Some say that as a consequence of the contact between the system and the hot reservoir, the system volume simply increases.

Taking $T_h$ and $T_{gas}$ as the temperatures of the reservoir and gas respectively.

Heat won't flow between two surfaces at exactly the same temperature, so $T_{gas}$ must be slightly less than $T_h$. Letting the gas expand (a volume increase) allows us to keep it at the same temperature while it absorbs the heat.

So the gas expands isothermally.

Some others (e.g. Chan, Al-Ghoul - Chemical thermodynamics) say the volume increase is due to a pressure lowering of the system.

This is a consequence of the volume increase described above, the pressure will be lowered.

Are those two diffent illustrations of the same concept? Why do we need to reduce the pressure (e.g. lowering the piston weight)?

Yes, they are both describing the same concept. We need to reduce the pressure/ increase the volume, in order to keep the gas at a temperature just less than that of the hot reservoir $T_h$

When the gas is being dumped into the cold reservoir, we need to minimise its entropy, so it's temperature is kept slightly higher than $T_c$, therefore as the heat leaves the gas, we need to compress it slightly, to keep it at this temperature.

• The strange thing is that the cited book says, about the isothermal expansion, Put the system in contact with the hot reservoir [...] and let the piston rise to volume V2 from volume V1 by reducing the external pressure from p1 to p2. My opinion is that reducing the pressure to a specific value is a way to control the gas expansion - i.e. it is a refinement of the Carnot cycle concept. Am I wrong? – Lo Scrondo Oct 4 '16 at 23:57
• No, I think you are correct. Let me check another book, what I wrote above was from my notes from Schroeder intro to thermal physics and it seems to make sense to me. I will edit the post citing another source if it agrees with my answer. – user108787 Oct 5 '16 at 0:35

These two statements are the same. The reason is this: under same temperature, if you increase volume, you have to reduce pressure. Otherwise you cannot keep the temperature. Using ideal gas for example $PV=nRT$.