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Carnot Cycle: Step 2-3: Adiabatic Expansion

An insulated cylinder containing the working fluid.

Step 1-2 is an isothermal, reversible expansion that occurs when a weight is removed from the back of the piston and heat flows into the working fluid from the hot reservoir.

This PV diagram shows the location of state 1 at high pressure and low specific volume.

In state 2b, insulation is added to the outside of the cylinder so step 2-3 will be adiabatic.

Piston-and-cylinder diagram showing state 2.

Piston-and-cylinder diagram showing the initial state, state 1.

As the pressure slowly decreases, the fluid slowly expands and the temperature drops.

This process is a reversible, adiabatic expansion.

State 3 is represented in this piston-and-cylinder diagram.

Lesson
6E Blog

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Lesson 6E: page 6 of 25

With the cylinder insulated, we pull more weight off the back of the piston.
The gas in the cylinder expands slowly.
The gas cools as it expands and no heat transfer occurs.
This is an adiabatic expansion and the curve connecting states 2 and 3 on the PV Diagram is called an adiabat.
Notice that the adiabat is steeper than the isotherm.
Does that make sense to you ?
Along the isotherm, heat is continuously added as the process moves from state 1 to state 2. This addition of heat causes the gas to expand little bit faster as the pressure drops. This shifts each point on the curve a little bit to the right. The result is that the isotherm is made less steep by the heat flowing in from the hot reservoir.
Along the adiabat, there is no flow of heat into the system, so the points on the curve are not shifted to the right and, voila, the adiabat is steeper than the isotherm!
Now, on with the cycle. What do you think the next step will be?
Remember that this is a cycle, so somehow the system must return to state 1.
The volume needs to decrease and the pressure needs to increase, so I hope you guessed that the next step will be a compression.
But what kind of compression?

Carnot Cycle: Step 2-3: Adiabatic Expansion

Ch 6, Lesson E, Page 6 - Carnot Cycle: Step 2-3: Adiabatic Expansion