Examples of ideal gas in the following topics:
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- 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 ).
- In an ideal gas, there is no molecule-molecule interaction, and only elastic collisions are allowed.
- Therefore, we derive a microscopic version of the ideal gas law
- Because the forces between them are quite weak at these distances, they are often described by the ideal gas law.
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- 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.
- Remember that the general gas equation only applies if the molar quantity of the gas is fixed.
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- Also, the temperature of an ideal monatomic gas is a measure of the average kinetic energy of its atoms, as illustrated in .
- The kinetic theory of gases uses the model of the ideal gas to relate temperature to the average translational kinetic energy of the molecules in a container of gas in thermodynamic equilibrium .
- In kinetic theory, the temperature of a classical ideal gas is related to its average kinetic energy per degree of freedom Ek via the equation:
- We will also derive the ideal gas law:
- (R: ideal gas constant, n: number of moles of gas) from a microscopic theory.
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- Temperature is directly proportional to the average translational kinetic energy of molecules in an ideal gas.
- We have seen in the Atom on "Origin of Pressure" that, for an ideal gas under our assumptions:
- What can we learn from this atomic and molecular version of the ideal gas law?
- Recall the macroscopic expression of the ideal gas law:
- Describe relationship between temperature and energy of molecules in an ideal gas
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- In ideal gases, there is no inter-particle interaction.
- Therefore, practical internal energy changes in an ideal gas may be described solely by changes in its translational kinetic energy.
- The average kinetic energy (KE) of a particle in an ideal gas is given as:
- Helium, like other noble gases, is a monatomic gas, which often can be described by the ideal gas law.
- Determine the number of degrees of freedom and calculate the internal energy for an ideal gas molecule
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- 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.
- In thermodynamics, the work involved when a gas changes from state A to state B is simply:
- 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.
- Conversely, if the environment does work on the system so that its internal energy increases, the work is counted as negative (for details on internal energy, check our Atom on "Internal Energy of an Ideal Gas").
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- 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
- 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.
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- 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
- 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.
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- 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:
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- 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).
- Therefore, the work done by the gas (W) is:
- 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").