In physics, engineering, and physical chemistry, a perfect gas is a theoretical gas model that differs from real gases in specific ways that makes certain calculations easier to handle. In all perfect gas models, intermolecular forces are neglected. This means that one can neglect many complications that may arise from the Van der Waals forces. All perfect gas models are ideal gas models in the sense that they all follow the ideal gas equation of state. However, the idea of a perfect gas model is often invoked as a combination of the ideal gas equation of state with specific additional assumptions regarding the variation (or nonvariation) of the heat capacity with temperature.
Perfect gas nomenclature The terms perfect gas and ideal gas are sometimes used interchangeably, depending on the particular field of physics and engineering. Sometimes, other distinctions are made, such as between thermally perfect gas and calorically perfect gas, or between imperfect, semi-perfect, and perfect gases, and as well as the characteristics of ideal gases. Two of the common sets of nomenclatures are summarized in the following table.
Thermally and calorically perfect gas Along with the definition of a perfect gas, there are also two more simplifications that can be made although various textbooks either omit or combine the following simplifications into a general "perfect gas" definition. For a fixed number of moles of gas n {\displaystyle n} , a thermally perfect gas
is in thermodynamic equilibrium is not chemically reacting has internal energy U {\displaystyle U} , enthalpy H {\displaystyle H} , and constant volume / constant pressure heat capacities C V {\displaystyle C_{V}} , C P {\displaystyle C_{P}} that are solely functions of temperature and not of pressure P {\displaystyle P} or volume V {\displaystyle V} , i.e., U = U ( T ) {\displaystyle U=U(T)} , H = H ( T ) {\displaystyle H=H(T)} , d U = C V ( T ) d T {\displaystyle dU=C_{V}(T)dT} , d H = C P ( T ) d T {\displaystyle dH=C_{P}(T)dT} . These latter expressions hold for all tiny property changes and are not restricted to constant- V {\displaystyle V} or constant- P {\displaystyle P} variations. A calorically perfect gas
is in thermodynamic equilibrium is not chemically reacting has internal energy U {\displaystyle U} , and enthalpy H {\displaystyle H} that are functions of temperature only, i.e., U = U ( T ) {\displaystyle U=U(T)} , H = H ( T ) {\displaystyle H=H(T)}
has heat capacities C V {\displaystyle C_{V}} , C P {\displaystyle C_{P}} that are constant, i.e., d U = C V d T {\displaystyle dU=C_{V}dT} , d H = C P d T {\displaystyle dH=C_{P}dT} and Δ U = C V Δ T {\displaystyle \Delta U=C_{V}\Delta T} , Δ H = C P Δ T {\displaystyle \Delta H=C_{P}\Delta T} , where Δ {\displaystyle \Delta } is any finite (non-differential) change in each quantity. It can be easily shown that an ideal gas (i.e. satisfying the ideal gas equation of state, P V = n R T {\displaystyle PV=nRT} ) is either calorically perfect or thermally perfect. This is because the internal energy of an ideal gas is at most a function of temperature, as shown by the thermodynamic equation
( ∂ U ∂ V ) T = T ( ∂ S ∂ V ) T − P = T ( ∂ P ∂ T ) V − P , {\displaystyle \left({{\partial U} \over {\partial V}}\right)_{T}=T\left({{\partial S} \over {\partial V}}\right)_{T}-P=T\left({{\partial P} \over {\partial T}}\right)_{V}-P,}
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