isotherm

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.