adiabatic index

(noun)

The ratio of the heat capacity at constant pressure to heat capacity at constant volume.

Related Terms

Examples of adiabatic index in the following topics:

  • Specific Heat for an Ideal Gas at Constant Pressure and Volume

    • The heat capacity ratio or adiabatic index is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.

  • Adiabatic Processes

    • In our Atom on "Adiabatic Processes" (category: the First Law of Thermodynamics), we learned that an adiabatic process is any process occurring without gain or loss of heat within a system.
    • We also learned a monatomic ideal gas expands adiabatically.
    • A strong magnetic field is applied to adiabatically align magnetic moments of the particles in the gas.
    • The magnetic field is reduced adiabatically, and thermal energy of the gas causes "ordered" magnetic moments to become random again.
    • This scheme is called adiabatic demagnetization cooling.

  • Adiabatic Processes

    • An adiabatic process is any process occurring without gain or loss of heat within a system.
    • In contrast, an adiabatic process is where a system exchanges no heat with its surroundings (Q = 0).
    • (See our atom on "Adiabatic Process. ") In other words, in an isothermal process, the value ΔT = 0 but Q ≠ 0, while in an adiabatic process, ΔT ≠ 0 but Q = 0.

  • Detonation Waves

    • The lower curve $a$ is the shock adiabat without the chemical changes and $a'$ is the detonation abiabat which uses the functional form of the enthalpy in the burnt gas.
    • The detonation adiabat below the Jouguet point $E$ cannot be reached if the combustion begins after the gas is compressed.
    • Shock (Hugoniot) Adiabat (in gray), Detonation Adiabat (in black) and Standard (Poisson) Adiabat (in blue).

  • Isothermal Processes

    • In contrast, an adiabatic process is where a system exchanges no heat with its surroundings (Q = 0).
    • (See our atom on "Adiabatic Process. ") In other words, in an isothermal process, the value ΔT = 0 but Q ≠ 0, while in an adiabatic process, ΔT ≠ 0 but Q = 0.

  • Radiative Shocks

    • Again we still have the relationships between the flux, velocities, slopes and areas on the plane that result from the conservation of momentum and mass, but the shock adiabat is replaced with an isotherm as shown in Figure 12.4.
    • Because the standard adiabats are generally steeper than the isotherms, the gas always leaves the shock subsonically.
    • Isotherm (in black), Shock (Hugoniot) Adiabat (in gray), Standard (Poisson) Adiabats (in blue).

  • Carnot Cycles

    • The Carnot cycle comprises two isothermal and two adiabatic processes.
    • Recall that both isothermal and adiabatic processes are, in principle, reversible .
    • PV diagram for a Carnot cycle, employing only reversible isothermal and adiabatic processes.

  • Price Indices and the Rate of Change of Prices

    • Most often, the base period for an index is a single year and normalized.
    • The Laspeyres index and the Paasche index are two price indexes that attempt to compensate for this difficulty.
    • Using the example above, the base period index would be 5*10+8*1.5+2*40=142, and the current period index would be 5*12+8*2+2*45 = 166.
    • Again, using the above example, the base period index would be 4*10+6*1.5+2*40=129, and the current period index would be 4*12+6*2+2*45=150.
    • Two common price indices are the Consumer Price Index (CPI) and the Producer Price Index (PPI).

  • Problems

    • You can consider the flow to be adiabatic.

  • Non-relativistic Shocks

    • Figure 12.1 depicts the shock or Hugoniot adiabat for a shock with a preshock pressure $p_1$ and specific volume $V_1$.
    • There are two (or no) shock adiabats that connect any two points in the $p-V-$plane.
    • Figure 12.1 shows the curves of constant entropy or standard (Poisson) adiabats on the $p-V-$plane corresponding to the values of the entropy at $(p_1,V_1)$, $s_1$, and at $(p_2,V_2)$, $s_2$.
    • Because all of the adiabats are concave up in the $p-V-$plane, the slope of the secant must be larger than that of the tangent at $(p_1,V_1)$, so the flow enters the shock supersonically.
    • Shock (Hugoniot) Adiabats (in black) and Standard (Poisson) Adiabats (in blue)