How Can You Design an Adiabatic and Reversible Thermodynamic System?

[decerto]

Homework Statement

Design an explicit system which does the following: It goes adiabatically and reversibly from state A to B. Then it returns from state B to state A probably irreversibly and receiving some heat from the outside world on the way. It can't give out heat.

Homework Equations

$PV^{\gamma}=c$ for an adiabatic process
$PV=c$ for an isothermal process

The Attempt at a Solution

[/B]
I attempted to draw various 3 step PV diagrams using isobaric and isochoric steps but they all gave out heat. The only way I can think of doing this is if the adiabatic process is the same as an isothermal process i.e
$PV^{\gamma}=PV$
$\gamma=1$
$C_p=C_v$

But this can't be true for an ideal gas so I have no idea.

 

[DrClaude]

I attempted to draw various 3 step PV diagrams using isobaric and isochoric steps but they all gave out heat.

Doesn't that depend on the direction of the process?

 

[decerto]

Doesn't that depend on the direction of the process?

Yes but amn't I forced into a direction that gives out heat after an adiabatic process then a process which takes in heat if I want to get back to the start?

 

[DrClaude]

Yes but amn't I forced into a direction that gives out heat after an adiabatic process then a process which takes in heat if I want to get back to the start?

I haven't worked out the details, but if your adiabatic process is an expansion, can't you go back to state A without any heat leaving the system?

 

[HalfLostAndSearching]

I would like to clarify the concept of an adiabatic process and suggest a solution to this problem. An adiabatic process is one in which there is no transfer of heat between the system and its surroundings. This means that the system is thermally insulated, and any change in its internal energy is solely due to work done on or by the system.

To design a system that goes adiabatically and reversibly from state A to B, we can use a piston-cylinder setup filled with an ideal gas. The piston is initially at position A, and the gas is in equilibrium with its surroundings at a pressure P_A and volume V_A. To go from state A to B adiabatically, we can slowly compress the gas by pushing the piston in, while keeping the surroundings at a constant temperature. This will cause the gas to heat up and reach a final state B with a higher pressure P_B and a smaller volume V_B.

To return from state B to A, we can use a heat exchanger to transfer heat from the surroundings to the gas, while keeping the pressure constant at P_B. This will cause the gas to expand isobarically, reaching a state C with a larger volume V_C and the same pressure P_B. Finally, we can slowly push the piston back to its original position A, while keeping the surroundings at a constant temperature. This will cause the gas to cool down and reach the original state A with a lower pressure P_A and the same volume V_A.

It is important to note that the process from B to C is not reversible, as heat is transferred from the surroundings to the system. However, the overall process from A to B to C and back to A is reversible, as the system returns to its original state and there is no net transfer of heat. Therefore, this system satisfies the requirements of going adiabatically and reversibly from state A to B and back to A, while receiving heat from the outside world only during the irreversible step from B to C.