ideal gas constant

Examples of ideal gas constant in the following topics:

• 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.
  • 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.
  • 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.

• 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:
  • The heat capacity at constant pressure of 1 J·K−1 ideal gas is:
  • For an ideal gas, evaluating the partial derivatives above according to the equation of state, where R is the gas constant for an ideal gas yields:

• The Ideal Gas Equation

  • In real life, there is no such thing as a truly ideal gas, but at high temperatures and low pressures (conditions in which individual particles will be moving very quickly and be very far apart from one another so that their interaction is almost zero), gases behave close to ideally; this is why the Ideal Gas Law is such a useful approximation.
  • R is the ideal gas constant, which takes on different forms depending on which units are in use.
  • The ideal gas equation enables us to examine the relationship between the non-constant properties of ideal gases (n, P, V, T) as long as three of these properties remain fixed.
  • For the ideal gas equation, note that the product PV is directly proportional to T.
  • Discusses the ideal gas law PV = nRT, and how you use the different values for R: 0.0821, 8.31, and 62.4.

• 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).
  • For an ideal gas, this means the volume of a gas is proportional to its temperature (historically, this is called Charles' law).
  • Using the ideal gas law PV=NkT (P=const),
  • (Eq. 3; for the details on internal energy, see our Atom on "Internal Energy of an Ideal Gas").

• Density Calculations

  • A reformulation of the Ideal Gas Equation involving density allows us to evaluate the behaviors of ideal gases of unknown quantity.
  • The Ideal Gas Equation in the form $PV=nRT$ is an excellent tool for understanding the relationship between the pressure, volume, amount, and temperature of an ideal gas in a defined environment that can be controlled for constant volume.
  • We know the Ideal Gas Equation in the form $PV=nRT$.
  • The term $\frac{m}{V}$ appears on the right-hand side of the above rearranged Ideal Gas Law.
  • Atmospheric science offers one plausible real-life application of the density form of the ideal gas equation.

• Expressing the Equilibrium Constant of a Gas in Terms of Pressure

  • For gas-phase reactions, the equilibrium constant can be expressed in terms of partial pressures, and is given the designation KP.
  • For gas-specific reactions, however, we can also express the equilibrium constant in terms of the partial pressures of the gases involved.
  • The reason we are allowed to write a K expression in terms of partial pressures for gases can be found by looking at the ideal gas law.
  • Recall that the ideal gas law is given by:
  • Note that in order for K to be constant, temperature must be constant as well.

• Equations of State

  • The ideal gas law is the equation of state of a hypothetical ideal gas (in which there is no molecule to molecule interaction).
  • 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
  • The proportionality factor is the universal gas constant, R, i.e.
  • Therefore, we derive a microscopic version of the ideal gas law

• The Effect of the Finite Volume

  • Real gases deviate from the ideal gas law due to the finite volume occupied by individual gas particles.
  • The ideal gas law is commonly used to model the behavior of gas-phase reactions.
  • The van der Waals equation modifies the ideal gas law to correct for this excluded volume, and is written as follows:
  • The available volume is now represented as $V - nb$, where b is a constant that is specific to each gas.
  • The constant b is defined as:

• Problem Solving

  • With the ideal gas law we can figure pressure, volume or temperature, and the number of moles of gases under ideal thermodynamic conditions.
  • 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.
  • Variations of the ideal gas equation may help solving the problem easily.
  • where N is the number of particles in the gas and k is the Boltzmann constant.