gas constant

Examples of gas constant in the following topics:

• Constant Pressure

  • Isobaric processis a thermodynamic process in which the pressure stays constant (at constant pressure, work done by a gas is $P \Delta V$).
  • 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).
  • Let's consider a case in which a gas does work on a piston at constant pressure P, referring to Fig 1 as illustration.
  • Specific heat at constant pressure is defined by the following equation:
  • By noting that N=NAn and R = kNA (NA: Avogadro's number, R: universal gas constant), we derive:

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

  • An ideal gas has different specific heat capacities under constant volume or constant pressure conditions.
  • Specific Heat for an Ideal Gas at Constant Pressure and Volume
  • The heat capacity at constant volume of nR = 1 J·K−1 of any gas, including an ideal gas is:
  • For moderate temperatures, the constant for a monoatomic gas is cv=3/2 while for a diatomic gas it is cv=5/2 (see ).
  • The heat capacity at constant pressure of 1 J·K−1 ideal gas is:

• Equations of State

  • The ideal gas law is the equation of state of a hypothetical ideal gas (an illustration is offered in ).
  • while Charles' law states that volume of a gas is proportional to the absolute temperature T of the gas at constant pressure
  • where C is a constant which is directly proportional to the amount of gas, n (representing the number of moles).
  • The proportionality factor is the universal gas constant, R, i.e.
  • where k is Boltzmann's constant and N is the number of molecules.

• Isothermal Processes

  • For an ideal, the product of pressure and volume (PV) is a constant if the gas is kept at isothermal conditions.
  • The value of the constant is nRT, where n is the number of moles of gas present and R is the ideal gas constant.
  • In other words, the ideal gas law PV = nRT applies.
  • In thermodynamics, the work involved when a gas changes from state A to state B is simply
  • It is also worth noting that, for many systems, if the temperature is held constant, the internal energy of the system also is constant, and so $\Delta U = 0$.

• Overview of Temperature and Kinetic Theory

  • The kinetic theory of gases describes a gas as a large number of small particles (atoms and molecules) in constant, random motion.
  • The kinetic theory of gases describes a gas as a large number of small particles (atoms or molecules), all of which are in constant, random motion.
  • (k: Boltzmann's constant).
  • We will also derive the ideal gas law:
  • (R: ideal gas constant, n: number of moles of gas) from a microscopic theory.

• Constant Pressure and Volume

  • Isobaric process is one in which a gas does work at constant pressure, while an isochoric process is one in which volume is kept constant.
  • A process in which a gas does work on its environment at constant pressure is called an isobaric process, while one in which volume is kept constant is called an isochoric process.
  • Since the pressure is constant, the force exerted is constant and the work done is given as PΔV.
  • If a gas is to expand at a constant pressure, heat should be transferred into the system at a certain rate.
  • An isobaric expansion of a gas requires heat transfer during the expansion to keep the pressure constant.

• Adiabatic Processes

  • An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0.
  • For an ideal, the product of pressure and volume (PV) is a constant if the gas is kept at isothermal conditions.
  • The value of the constant is nRT, where n is the number of moles of gas present and R is the ideal gas constant.
  • In other words, the ideal gas law PV = nRT applies.
  • It is also worth noting that, for many systems, if the temperature is held constant, the internal energy of the system also is constant, and so $\Delta U = 0$.

• Problem Solving

  • The Ideal Gas Law is the equation of state of a hypothetical ideal gas.
  • where R is the universal gas constant, and with it we can find values of the pressure P, volume V, temperature T, or number of moles n under a certain ideal thermodynamic condition.
  • where N is the number of particles in the gas and k is the Boltzmann constant.
  • Remember that the general gas equation only applies if the molar quantity of the gas is fixed.
  • For example, if a gas is mixed with another gas, you may have to apply the equation separately for individual gases.

• Isotherms

  • An isothermal process is a change of a system in which the temperature remains constant: ΔT = 0.
  • For an ideal gas, the product PV (P: pressure, V: volume) is a constant if the gas is kept at isothermal conditions (Boyle's law).
  • According to the ideal gas law, the value of the constant is NkT, where N is the number of molecules of gas and k is Boltzmann's constant.
  • This means that $p = {N k T \over V} = {\text{Constant} \over V}$ holds.
  • (This equation is derived in our Atom on "Constant Pressure" under kinetic theory.

• Radiative Shocks

  • The opposite extreme is that the shock heats the gas sufficiently that radiative losses are important near the shock and the gas rapidly cools.
  • Astrophysically the rate that gas cools can depend very sensitively on the temperature of the gas.
  • In particular gas above about $10^4$~K radiates much more effectively than cooler gas.
  • From the diagram it is apparent that the entropy of the gas decreases through an isothermal shock; as a gas is compressed at constant temperature, its entropy decreases.
  • Sometimes the temperature of the gas is held constant through the interaction with an external radiation field, so that even slight departures from isothermality disappear on a short timescale.