A Space Model of the Carnot Cycle E. W. KANNING a n d R. J. HARTMAN Indiana University, Bloomington, Indiana ICOLAS Leonard Sadi Carnot published in his m e m o d in 1824theconclusions which verified the fundamental concepts of the First and Second Laws of Thermodynamics. He considered the ideal cyclic process involving the reversible conversion of heat into work, which now bears his name and which constitutes a portion of the section on thermodynamics in any physical chemistry textbook.
N
.
It is the purpose of this article to present a model of a typical Carnot cycle in order to show more clearly the four steps of this process. The cycle involves changes of pressure, volume, and temperature, and therefore a two-dimensional drawing is not wholly adequate. The model, shown in the photograph (Figure l ) , is made of plaster of Paris set on a wooden base. The cycle, ABCD, is clearly shown on the face of the model. ' CARNOT, "R6ilexions sur la puissance motrice de deu et sur les machines prapres
dbvelopper cette puissance." Paris, 1824.
Figures 2, 3, 4, 5, and 6 are labeled to correspond to those faces as shown in Figure 1 ; the dimensions given in centimeters are those of the model from which the photograph was taken.
According to this model, the cycle begins a t point A a t which there is one mol of a perfect gas (hydrogen) a t 546'K. and two atmospherk pressure. As the gas is allowed to expand isothermally and reversibly a t this temperature, the volume and pressure change along the line AB until the point B is reached where the pressure is one atmosphere and the volume is 44.8 liters. The second step of the cycle begins a t point B where an adiabatic expansion takes place while the temperature is lowered from 546°K. to 273°K. For this adiabatic expansion of a perfect gas the equation PIn
where
=
2.639
r = Cp/Cv
-
1.4
is true and thus the curve BC is outlined on the face of the model.
The third step is an isothermal reversible compression of the gas as shown along the line CD;since the tempera-
sion such that the final volume is equal to the original volume. For this adiabatic compression the equation PT" = 2.000
is true and is shown as the curve DA on the model.
When the cycle ABCD is projected on the pressurevolume plane, i t appears as shown in Figure 7. The shape of this diagram results from the actual changes in pressure and volume through which the perfect monatomic gas passes.
ture remains constant (273OK.),,the pressure must increase as the volume decreases.
I
I I '4 v,
'4
FIGURE 7.-THE CARNOTCYCLEI N VOLWHEPLANE
The fourth step of the cycle is an adiabatic compres-
" 3
VOLUME TEE
PRBSSURE-
Since the mathematical develo~mentand use of the Carnot cycle in thermodynamics is adequately described in the better texts on physical chemisky and thermodynamics, this treatment is omitted.
