Ideal Carnot engine

The reactants enter the CSTR at the bath temperature, react in the CSTR and raise the temperature. The thermal engine is supposed to operate as an ideal Carnot engine, see [2]. The stoichiometric ratio of oxygen to methane is taken to be 2 1 and the evolution equations [1] of the temperature and concentrations are... 

It follows that the efficiency of the Carnot engine is entirely determined by the temperatures of the two isothermal processes. The Otto cycle, being a real process, does not have ideal isothermal or adiabatic expansion and contraction of the gas phase due to the finite thermal losses of the combustion chamber and resistance to the movement of the piston, and because the product gases are not at tlrermodynamic equilibrium. Furthermore the heat of combustion is mainly evolved during a short time, after the gas has been compressed by the piston. This gives rise to an additional increase in temperature which is not accompanied by a large change in volume due to the constraint applied by tire piston. The efficiency, QE, expressed as a function of the compression ratio (r) can only be assumed therefore to be an approximation to the ideal gas Carnot cycle. 

Although the Carnot cycle is useful in determining the ideal behavior of an ideal heat engine, it is not a practical cycle to use in the design of heat... 

A hypothetical cycle for achieving reversible work, typically consisting of a sequence of operations (1) isothermal expansion of an ideal gas at a temperature T2 (2) adiabatic expansion from T2 to Ti (3) isothermal compression at temperature Ti and (4) adiabatic compression from Ti to T2. This cycle represents the action of an ideal heat engine, one exhibiting maximum thermal efficiency. Inferences drawn from thermodynamic consideration of Carnot cycles have advanced our understanding about the thermodynamics of chemical systems. See Carnot s Theorem Efficiency Thermodynamics... 

In Chapter 2, we have analyzed one particular type of heat engine, the reversible Carnot cycle engine with an ideal gas as the working substance, and found that its efficiency is e = 1 — Tc/Th. For both practical and theoretical reasons, we ask if it is possible, with the same two heat reservoirs, to design an engine that achieves a higher efficiency than the reversible Carnot cycle, ideal gas engine. What can thermodynamics tell us about this possibility ... 

The ideal work of the process is that of a Carnot engine operating between the temperature of the refrigerated space and the temperature of the surroundings. 

The thermodynamic efficiency of a fuel cell is defined as the ratio between AG° and the enthalpy of reaction, AH°, p = AG°IAH°, and is not, unlike thermal external or internal combustion engines, limited by the ideal Carnot cycle. 

The cycle traversed by an ideal gas serving as the working fluid in a Carnot engine is shown by a PV diagram in Fig. 5.3. It consists of four reversible steps ... 

A certain Carnot engine requires 18 kg of water in the form of steam as its working substance. When 5 x 105 J of heat energy are added at a constant temperature of 400 K the gas expands to 4 m3. What is the approximate pressure of the gas after the initial expansion (The ideal gas constant is R = 8.314 J/K mol)... 

An example of a process that can deliver work by absorbing heat from a hot reservoir and rejecting heat to a cold reservoir is the Carnot engine. This is an idealized model consisting of a sequence of processes, each of which is assumed to be reversible. A reversible process is one that can be reversed by an infinitesimal change in the external conditions. For instance, in order to compress a gas reversibly, the external pressure at any moment should be P -i- AP, where P is the gas pressure at that moment and AP is a small pressure increment. The reversible compression can be changed to a reversible expansion by changing the external pressure to P - AP. A reversible... 

In Chapter 5 we said that Carnot s classic model of an idealized heat engine resulted in the following properties of the entropy function ... 

Using the statistical mechanical approach, we have been able to rederive equations (6.18)-(6.20) without any mention of steam engines or idealized Carnot cycles. These equations form the basis for much of the rest of thermodynamics, as we have already begtm to see in Chapter 5. These few relationships are so useful because they serve as pointers or criteria for the spontaneous direction of any process. Hopefully the statistical approach clarifies much of this, in the sense that we conceive of entropy as a measure of disorder or randomness. The most random permissible state is also the most probable statistically. It is self-evident that spontaneous processes head in the most probable direction by doing so, they maximize entropy. 

If an ideal gas is used as the working substance in a Carnot engine, the application of the first law to each of the steps in the cycle can be written as in Table 8.3. The values of and FF3, which are quantities of work produced in an isothermal reversible expansion of an ideal gas, are obtained from Eq. (7.6). The values of AC are computed by integrating the equation dU = C dT. The total work produced in the cycle is the sum of the individual quantities. 

Carnot Cycle - An ideal heat engine (conceived by Sadi Carnot) in which the sequence of operations forming the working cycle consists of isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression back to its initial state. 

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