In fact, the temperature increases can be so large that the mixture can explode without the addition of a spark. Integrating this relationship between the limits 1 and 2 on an isentrop, we obtain: The isentropic exponent for an ideal gas is determined in the following way.
Applying then a method similar to that described above, from Eq. The relation between the temperatures T 1 and T 2 at the two points on the isentrop can be found as follows. In Fig. Since for an ideal gas, as follows from Clapeyron's equation,. The values of A: To elucidate this problem, it is necessary to formulate the differential equation of an isentropic process.
The gas will then be in adiabatic flow since no heat is added to it from the outside and no heat is rejected from the gas to the surroundings.
The isentropic exponent k whose value by itself can be used as a property of state happens to differ significantly for substances in different states of aggregation. The formula for work performed in an isentropic process, l 1-2 , can be presented in another form.
This relationship is called the Poisson equation of an adiabat. Therefore, when an ideal gas expands freely, its temperature does not change; this is also called a Joule expansion. The slope of the curve at any point is.
A thermodynamic system in which an adiabatic process proceeds can be visualized as a certain volume confined by boundaries fitted with ideal heat insulation through which no heat transfer can take place; boundaries of this kind are said to be adiabatic. Thus, by Eq.
It will be emphasized once more that Eqs. Gasoline vapor is injected into the cylinder of an automobile engine when the piston is in its expanded position.
These relationships can be used to obtain. For an ideal gas the formulas for the work of expansion can be represented in a different form.