2.5 Thermodynamic Engines
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namely, a series of four steps by which the thermodynamic system (or ‘working
substance’) is taken from an initial thermodynamic state to a final thermodynamic
state coincident with the initial state. The four steps in the Carnot cycle are thus:
1. a reversible isothermal expansion in thermal contact with the thermal reservoir
characterized by temperature T = T high ;
2. a reversible adiabatic expansion in which the temperature of the system decreases
from T high to T low ;
3. a reversible isothermal compression in thermal contact with the thermal reservoir
characterized by temperature T = T low ;
4. a reversible adiabatic compression in which the system temperature increases
from T low to T high , and the system is returned to its initial thermodynamic state.
The importance of the Carnot cycle in applied thermodynamics is reflected in the
Carnot Theorem, which states that
All Carnot cycles operating between the same temperature have the same efficiency.
Note that there is no caveat on this theorem to limit its range of validity by, for
example, restricting it to ideal gases or to fluids. Proofs of this theorem may be found
in many standard thermodynamics textbooks, such as that by Klotz and Rosenberg
[1]. The fact that the Carnot cycle provides a means for measuring the ratio of
two temperatures implies that a temperature scale may be established relative to an
arbitrary multiplicative constant, so that the assignation of a specific value for the
temperature of an arbitrarily chosen standard system then allows the temperatures
of all other systems to be determined uniquely in terms of values that are directly
proportional to the temperature chosen for the standard system [1, 7]. The absolute
(or Kelvin) temperature scale was established in this manner by Lord Kelvin in
1854, by assigning the value 273.16 ◦ to the triple point 7 of water.
It is perhaps worth commenting at this point on the continued use of Celsius
temperatures in many aspects of engineering research and practice, including the
measurement and reporting of thermodynamic properties. The Celsius temperature
scale (units ◦ C), which can be related to the absolute thermodynamic (or Kelvin)
temperature scale via the prescription T / ◦ C T /K − 273.15, allows negative
temperatures, has an incorrect zero and, although it gives temperature differences
correctly, it gives incorrect temperature ratios. Thus, as has been emphasized by
Callen [7], it really does not qualify as a thermodynamic temperature scale.
The Carnot Cycle for a Classical Ideal Gas
In general, a Carnot cycle consists of a sequence of reversible expansions and
compressions beginning with and ending at a particular thermodynamic state,
7 The triple point for a substance is defined as the temperature and pressure at which its solid,
liquid, and gas phases are in thermodynamic equilibrium.
55
namely, a series of four steps by which the thermodynamic system (or ‘working
substance’) is taken from an initial thermodynamic state to a final thermodynamic
state coincident with the initial state. The four steps in the Carnot cycle are thus:
1. a reversible isothermal expansion in thermal contact with the thermal reservoir
characterized by temperature T = T high ;
2. a reversible adiabatic expansion in which the temperature of the system decreases
from T high to T low ;
3. a reversible isothermal compression in thermal contact with the thermal reservoir
characterized by temperature T = T low ;
4. a reversible adiabatic compression in which the system temperature increases
from T low to T high , and the system is returned to its initial thermodynamic state.
The importance of the Carnot cycle in applied thermodynamics is reflected in the
Carnot Theorem, which states that
All Carnot cycles operating between the same temperature have the same efficiency.
Note that there is no caveat on this theorem to limit its range of validity by, for
example, restricting it to ideal gases or to fluids. Proofs of this theorem may be found
in many standard thermodynamics textbooks, such as that by Klotz and Rosenberg
[1]. The fact that the Carnot cycle provides a means for measuring the ratio of
two temperatures implies that a temperature scale may be established relative to an
arbitrary multiplicative constant, so that the assignation of a specific value for the
temperature of an arbitrarily chosen standard system then allows the temperatures
of all other systems to be determined uniquely in terms of values that are directly
proportional to the temperature chosen for the standard system [1, 7]. The absolute
(or Kelvin) temperature scale was established in this manner by Lord Kelvin in
1854, by assigning the value 273.16 ◦ to the triple point 7 of water.
It is perhaps worth commenting at this point on the continued use of Celsius
temperatures in many aspects of engineering research and practice, including the
measurement and reporting of thermodynamic properties. The Celsius temperature
scale (units ◦ C), which can be related to the absolute thermodynamic (or Kelvin)
temperature scale via the prescription T / ◦ C T /K − 273.15, allows negative
temperatures, has an incorrect zero and, although it gives temperature differences
correctly, it gives incorrect temperature ratios. Thus, as has been emphasized by
Callen [7], it really does not qualify as a thermodynamic temperature scale.
The Carnot Cycle for a Classical Ideal Gas
In general, a Carnot cycle consists of a sequence of reversible expansions and
compressions beginning with and ending at a particular thermodynamic state,
7 The triple point for a substance is defined as the temperature and pressure at which its solid,
liquid, and gas phases are in thermodynamic equilibrium.