isotherm

(noun)

in thermodynamics, a curve on a P-V diagram representing the state of a gas at constant temperature ("iso-" means same and "-therm" refers to temperature)

Related Terms

  • specific heat
  • critical point
  • Boyle's law
  • ideal gas

(noun)

in thermodynamics, a curve on a p-V diagram for an isothermal process

Related Terms

  • specific heat
  • critical point
  • Boyle's law
  • ideal gas

Examples of isotherm in the following topics:

  • Isothermal Processes

    • An isothermal process is a change of a thermodynamic system, in which the temperature remains constant.
    • An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0.
    • For an isothermal, reversible process, this integral equals the area under the relevant pressure-volume isotherm, and is indicated in blue in for an ideal gas.
    • From the first law of thermodynamics, it follows that $Q =-W$ for this same isothermal process.
    • The blue area represents "work" done by the gas during expansion for this isothermal change.
  • Isotherms

    • An isothermal process is a change of a system in which the temperature remains constant: ΔT = 0.
    • An isothermal process is a change of a system in which the temperature remains constant: ΔT = 0.
    • Each curve is called an isotherm.
    • For an isothermal, reversible process, this integral equals the area under the relevant pressure-volume isotherm, and is indicated in blue in for an ideal gas.
    • The blue area represents "work" done by the gas during expansion for this isothermal change.
  • Adiabatic Processes

    • An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0.
    • Each curve is called an isotherm.
    • For an isothermal, reversible process, this integral equals the area under the relevant pressure-volume isotherm, and is indicated in blue in for an ideal gas.
    • From the first law of thermodynamics, it follows that $Q =-W$ for this same isothermal process.
    • The blue area represents "work" done by the gas during expansion for this isothermal change.
  • Radiative Shocks

    • Because the standard adiabats are generally steeper than the isotherms, the gas always leaves the shock subsonically.
    • This yields a minimum energy ratio for the isothermal shock of
    • Even this weakest of isothermal shocks results in a compression ratio $\rho_2/\rho_1 = \gamma$.
    • However, the enthalpy of an isothermal gas is given by
    • Isotherm (in black), Shock (Hugoniot) Adiabat (in gray), Standard (Poisson) Adiabats (in blue).
  • Real Gases

    • This law sufficiently approximates gas behavior in many calculations; real gases exhibit complex behaviors that deviate from the ideal model, however, as shown by the isotherms in the graph below.
    • (Isotherms refer to the different curves on the graph, which represent a gas' state at different pressure and volume conditions but at constant temperature; "Iso-" means same and "-therm" means temperature—hence isotherm.)
    • Note that the isotherms representing high temperatures deviate less from ideal behavior (Z remains close to 1 across the graph), while for isotherms representing low temperatures, Z deviates greatly from unity.
    • Notice that the higher isotherms on the graph, which represent the gas' state at higher temperature, show the typical, concave decreasing curve of an inverse relationship.
    • As temperature decreases, however, the isotherms on the lower portion of the graph significantly deviate from this ideal inverse relationship between P and V.
  • 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.
    • Heat transfer Qh occurs into the working substance during the isothermal path AB, which takes place at constant temperature Th.
    • Heat transfer Qc occurs out of the working substance during the isothermal path CD, which takes place at constant temperature Tc.
  • Van der Waals Equation

    • Isotherm (plots of pressure versus volume at constant temperature) can be produced using the van der Waals model.
  • Vertical Structure

    • This is essentially assuming that the disk is isothermal vertically.
    • The relative thickness of the disk remains nearly constant with radius if only internal heating is important in a vertically isothermal disk.
  • Winds

    • One can assume that the stellar wind is approximately isothermal ($\gamma=1$)—if one assumes otherwise one gets the Bernouli equation from the section on spherical accretion.
    • The velocity structure for an isothermal wind, neglecting angular momentum magnetic fields.
  • Constant Pressure

    • For example, an ideal gas that expands while its temperature is kept constant (called isothermal process) will exist in a different state than a gas that expands while pressure stays constant (called isobaric process).
    • We will discuss isothermal process in a subsequent Atom.
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