(Image from: https://aerospaceamerica.aiaa.org/year-in-review/advances-made-toward-rotating-detonation-engines/)

Explanation of a RDE, with thermodynamics starting at 6m 27s: https://www.youtube.com/watch?v=rG_Eh0J_4_s

The Carnot Cycle

For a reversible cycle,

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The Carnot Cycle A Carnot cycle is a particular type of internally reversible cycle (can be a power, refrigeration, or heat pump cycle). Each of the process steps is assumed to be internally reversible, e.g.,

• frictionless and no viscosity • quasi-equilibrium • expansions/compressions occur very slowly • heat addition/removal occur over a negligible temperature difference

Real cycles have irreversibilities that make them less efficient than a Carnot cycle.

hot res., TH

cold res., TC

QC,cycle

QH,cycle

Wbycycle

Carnot Power Cycle 1 – 2: isothermal expansion at TH 2 – 3: adiabatic expansion to TC

3 – 4: isothermal compression at TC

4 – 1: adiabatic compression to TH

Qin,1-2 Wby,1-2

hot r

eser

voir,

TH

Wby,2-3 Qout,3-4 Won,3-4

cold

rese

rvoi

r, T C

Won,4-1

Carnot Power Cycle shown for a substance that remains a vapor

C. Wassgren Last Updated: 2016 Dec 18 Chapter 03: Basic Thermodynamics

7.4 Carnot Cycle The Carnot Cycle is one particular type of internally reversible cycle. Being that it’s reversible, it serves as an ideal point of comparison for real cycles. A Carnot cycle consists of the following four internally reversible processes:

Process 1 – 2: isothermal expansion at TH From the 1st Law: .

ΔUsys,12 = 0 since the temperature remains constant during the process. Since Wby

sys,12 > 0 (expansion), Qinto sys,12 > 0 (heat addition). Process 2 – 3: adiabatic expansion (Q23 = 0)

From the 1st Law: .

Since Wby sys,23 > 0 (expansion), ΔUsys,23 < 0 ⇒ U3 < U2. Process 3 – 4: isothermal compression at TC

From the 1st Law: .

ΔUsys,12 = 0 since the temperature remains constant during the process. Since Wby

sys,34 < 0 (compression), Qinto sys,34 < 0 (heat rejection). Process 4 – 1: adiabatic compression (Q41 = 0)

From the 1st Law: .

Since Wby sys,41 < 0 (expansion), ΔUsys,41 > 0 ⇒ U4 > U1.

Following is a schematic of the process on a p-v diagram for a substance remaining entirely in the vapor phase throughout the cycle.

ΔUsys,12

=0⇥

=Qinto sys,12

−Wby sys,12

⇒Qinto sys,12

=Wby sys,12

ΔUsys,23

=Qinto sys,23

=0⇥⇤⌅

−Wby sys,23

⇒ΔUsys,23

= −Wby sys,23

ΔUsys,34

=0⇥

=Qinto sys,34

−Wby sys,34

⇒Qinto sys,34

=Wby sys,34

ΔUsys,41

=Qinto sys,41

=0⇥⇤⌅

−Wby sys,41

⇒ΔUsys,41

= −Wby sys,41

v

p

TH

TC

1

2

4

3

Carnot Power Cycle shown for a substance that is a SLVM

C. Wassgren Last Updated: 2016 Dec 18 Chapter 03: Basic Thermodynamics

Following are schematics of a simple vapor power Carnot cycle, where a change of phase does occur.

Notes: 1. It’s also possible to have Carnot refrigeration and heat pump cycles. 2. Since each of the processes in a Carnot cycle is internally reversible, the entire Carnot cycle is also

internally reversible. Hence, the efficiency and coefficients of performance of a Carnot cycle are given by,

η = ηrev = 1 – TC/TH, COPref = COPref,rev = TC/(TH – TC), COPhp = COPhp,rev = TH/(TH – TC).

3. In order to be internally reversible, the heat addition and removal processes with the thermal reservoirs must not occur over a finite temperature gradient, i.e., the temperature of the system must equal the temperature of the thermal reservoir during the heat addition and heat removal processes. In a real system, there must be some finite temperature difference to drive the heat transfer process, which is one reason a real cycle would not be reversible.

4. It’s possible for a system to have the same set of processes as the Carnot cycle (isothermal expansion, adiabatic expansion, isothermal compression, adiabatic compression), but not be reversible. In that case, the efficiency of the cycle will be less than the Carnot efficiency.

boiler

condenser

turbine pump/ compressor

1 2

3 4

v

p

TH

TC

1 2

3 4

hot reservoir, TH

cold reservoir, TC

heat exchanger

heat exchanger

Qout

Qin

turbine pump

cold reservoir @ TC

hot reservoir @ TH

Wby Won