Engineering Details of Heat Engines

A focus of Engineers has been the extensive research of numerous heat engine cycles. The goal is to enhance the amount of usable work from a given power source. Engineers have deliberated to work around the Carnot Cycle limit of the gas-based cycle. There has been at a few ways developed to possibly get around that limit to increase the efficiency. One way is to increase the temperature difference in the heat engine by increasing the hot reservoir temperature. This method is used in combined cycle gas turbines but environmental concerns of nitrogen oxides and physical limits of materials restricting maximum temperatures on the feasible heat engines. With these concerns in mind, modern turbines run at the maximum temperatures for physical properties such as melting point to not be reached and keeping the nitrogen oxides output within acceptable range.

Another method used to increase efficiency is to decrease the output temperature by use of mixed chemical working fluids and utilizing the shifting performance of the blends. An example of this is the Kalina Cycle which uses 70/30 mix of ammonia and water which permits the generation of valuable power.

Figure 1:

Fig. 9

(Figure 1 shows a simplified diagram of the Kalina cycle which is used to increase efficiency) (2)


Figure 2:

Fig. 10

(Figure 2 shows a temperature vs entropy plot of the Kalina Cycle) (3)


A third example engineers use to increase efficiency is to use the physical properties of the working fluid to the advantage of the heat engine. The most common way is to use water above the critical point (supercritical steam). The activities of fluids above this point changes dramatically and the behaviors can be used to extract better thermodynamic efficiency. The Chemical properties of the working fluids can also be used as an advantage for efficiency. Temperature can be increased denaturing a molecule into smaller units. This lowers the molecular weight of the fluid, in turn significantly increasing the efficiency of the heat engine. The fluid of lower molecular weight moves through the engine and is cooled by a heat sink which causes the molecules to reform into their original state and can be recycled back into the engine for reuse.

Heat Engine Processes (1)

Fig. 11

(Table 1 shows various heat engine processes. Each process is isothermal (constant temperature), isobaric (constant pressure), isochoric (constant volume), adiabatic (no heat added or removed), or isentropic (reversible adiabatic).) (1)



  1. “Heat Engine.” Wikipedia, Wikimedia Foundation, 4 Dec. 2018,
  2.  “Otec Explained.” What Is Biodiesel, Engineering Department University of Strathclyde in Glasgow, project/exports/otecex.html.
  3. Chiranjit Maji. “Kalina Cycle.” Research Gate, Research Gate 2018, 2016,

Heat Engine Efficiency

Assuming the working substance in the Carnot cycle is ideal gas, for each segment w, q, and ΔU are calculated to determine the efficiency. The efficiency of the reversible Carnot cycle is defined in Thermodynamics, Statistical Thermodynamics, & Kinetics second edition by Thomas Engel and Philip Reid, page number 83 as, “the ratio of the work output to the heat withdrawn from the hot reservoir”. The goal is for the payoff to be significantly more then what we put in but we are always faced with the problem of getting less out then we put in due to significant amounts of energy being transferred to the environment. The efficiency of a heat engine functioning reversibly is always less than one and is shown in the equation:

Ε= Fig. 4

(equation 5.4, Engel, Reid, pg 83)

This also proves that 100% heat taken from hot reservoir is not converted to work. This leads to two very significant progressions of the Second Law of Thermodynamics, the Kelvin- Planck formulation and Clausius statement. The Kelvin- Planck statement of the Second law states that heat cannot be converted into 100 percent work. This statement is illustrated in the following figure.

Fig. 5

The Clausius statement, an alternative but equivalent statement of the second law states that heat cannot flow from cold reservoir to hot. This statement along with proof that both statements are essentially equivalent is illustrated in the following figures.

Fig. 6

Fig. 7


With the working element being an ideal gas, for a Carnot heat engine the efficiency can be articulated exclusively in terms of reservoir temperatures as shown in the following equation:

Fig. 8

(equation 5.9, Engel, Reid, pg 84)

The two statements of the second law of thermodynamics along with equations 5.4 and 5.9 support that we cannot convert heat into 100% work in a reversible reaction.  The only way the efficiency will approach 1 is if T hot -> or T cold ->0 which is not producible in practice as stated in the kelvin statement..  Since the work for an engine in an irreversible cycle is less then the work in a cycle where the engine is working reversibly, ε irreversible< ε reversible<1.




Engel, Thomas, et al. Instructor Solutions Manual Thermodynamics: Statistical Thermodynamics, & Kinetics, 2nd Ed. 2nd ed., Prentice Hall, 2010.


The Carnot Cycle

This reversible cycle described is called the Carnot cycle after the French engineer who first studied such cycles. The cycle depicted in figure 3, is a PV diagram representation of the Carnot cycle. From point (a) to point (b) is called isothermal expansion. During his step gas absorbs heat from the reservoir at Ti. From point (b) to (c) is called adiabatic expansion. During this step the gas expands further and by the end of the step the gas has cooled to T2. In both of these steps work is being done on the surroundings. The third step from (c) to (d) is called isothermal compression where heat is absorbed by the cold reservoir and the work is now being done on the system. In the last step of the cycle from point (d) to (a), the gas is then compressed to its original volume in adiabatic compression. In this step work is also being done on the system and temperature returns to its original temp T1. For this engine to be useful, the network must be done on the surroundings. In other words, the magnitude of the first 2 steps (a->b and b->c) must be greater than the magnitude of the last two steps (c->d and d->a). The area inside of the cycle is the work done by the engine.

Fig. 3

  • Citation:
  • Engel, Thomas, and Philip Reid. Thermodynamics, Statistical Thermodynamics, & Kinetics. 2nd ed., Pearson Education Inc., 2010.

Thermodynamic Principle: Heat Engine

 A heat engine makes use of the properties of thermodynamics to transform heat into work. Some examples of a heat engine are: gasoline engines, diesel engines, jet engines, and steam turbines.

For these examples, fuel combustion releases chemical energy. That heat transfers throughout the gas within the cylinder (A). This process increases the gas’s temperature as well as its pressure, therefore, exerting a force on the movable piston. The gas within the cylinder does work on the outside world, as the piston moves (B). As such, heat transfer of energy to the gas ends with work being done.

To repeat this process, the piston needs to be returned to its starting point. Heat now transfers energy from the gas to the surroundings, so that the gas’s pressure decreases, and a force is exerted by the surroundings to push the piston back through some distance (C).

All heat engines go through a cyclical process (A process to bring a system back to the original state). For that to happen, heat transfers from the gas to the surroundings, decreasing temperature and pressure until the piston reverts to the starting position.

Heat engines do work by using the energy transferred by heat from a source. Heat transfers energy (Qh) from a high reservoir, whereas heat transfers unused energy (Qc) into a cold reservoir, and the work done by the engine is W. The temperature of the hot reservoir is Th and the temperature of the cold reservoir is Tc.

Figure 1:Fig. 1


As stated before, a cyclical process brings the system back to its initial conditions before restarting the cycle. As such the system’s internal energy, U, is the same at the beginning as it is at the end. Meaning.

Figure 2: Fig. 2

According to the first law of thermodynamics (). The net heat transfer is the energy transferred in the engine by heat from the hot reservoir minus what transferred out to the cold reservoir (). With no change in internal energy for a complete cycle, we have. That makes work equal to the net heat transfer () or ().

  • Citations
  • Texas Education Agency. “12.4 Applications of Thermodynamics: Heat Engines, Heat Pumps, and Refrigerators.” Texas Gateway for Online Resources, Texas Education Agency, 2007-2018,
  • Engel, Thomas, and Philip Reid. Thermodynamics, Statistical Thermodynamics, & Kinetics. 2nd ed., Pearson Education Inc., 2010.