Develop expressions for the specific enthalpy, internal...

Develop expressions for the specific enthalpy, internal energy, and entropy changes $\left[h\left(v_{2}, T\right)-h\left(v_{1}, T\right)\right],\left[u\left(v_{2}, T\right)-\right.$ $\left.u\left(v_{1}, T\right)\right],\left[s\left(v_{2}, T\right)-s\left(v_{1}, T\right)\right]$, using the (a) van der Waals equation of state. (b) Redlich-Kwong equation of state.

Develop expressions for the specific enthalpy, internal energy, and entropy changes $\left[h\left(v_{2}, T\right)-h\left(v_{1}, T\right)\right],\left[u\left(v_{2}, T\right)-\right.$ $\left.u\left(v_{1}, T\right)\right],\left[s\left(v_{2}, T\right)-s\left(v_{1}, T\right)\right]$, using the
(a) van der Waals equation of state.
(b) Redlich-Kwong equation of state.

Key Concepts

Thermodynamic_Properties_and_Departure_Functions

The internal energy, enthalpy, and entropy of a system can be expressed in terms of their deviations from ideal behavior. Departures functions quantify these differences, enabling the derivation of expressions for property changes (such as h(v2,T) - h(v1,T), u(v2,T) - u(v1,T), and s(v2,T) - s(v1,T)) by integrating the contributions of intermolecular forces and finite molecular volumes. This involves using fundamental thermodynamic relationships like u = u(T,v) and h = u + Pv, and integrating the appropriate derivatives along isothermal or other thermodynamic paths.

Thermodynamic_Integration

Developing expressions for changes in specific enthalpy, internal energy, and entropy involves integrating differential forms of the state functions, often by employing the first and second laws of thermodynamics. For real gases modeled by specific equations of state, these integrals are calculated by substituting the pressure and volume corrections provided by the equations, thereby yielding expressions that include terms accounting for the non-ideal behavior of the gas.

Redlich_Kwong_Equation

The Redlich-Kwong equation of state is another model that adapts the ideal gas law to better represent real gases, particularly at higher temperatures and moderate pressures. It modifies the attractive and repulsive interactions in a different manner compared to the van der Waals equation, thereby yielding distinct integrals when computing changes in thermodynamic properties.

Van_der_Waals_Equation

The van der Waals equation of state introduces corrections to the ideal gas law by accounting for the finite molecular volume and the intermolecular attractive forces. This equation is fundamental for understanding real gas behavior at moderate pressures and temperatures, and it is used to derive expressions for thermodynamic properties by modifying both the pressure and volume terms within the energy and entropy integrals.

Equation_of_State

An equation of state is a mathematical relationship among state properties such as pressure, volume, and temperature that characterizes the behavior of a fluid. For real gases, these equations incorporate corrections for molecular size and intermolecular forces, allowing for the prediction of property changes that deviate from ideal gas behavior.

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