Understanding Specific Internal Energy at Saturated Liquid State
In classical thermodynamics, evaluating fluid properties at phase boundaries is fundamental to analyzing energy systems, steam turbines, power generation cycles, and refrigeration setups. When a pure substance reaches its boiling threshold for a specified pressure, it exists in a saturated liquid state. The specific internal energy associated with this condition, denoted mathematically as $u_f$, represents the total microscopic kinetic and potential energy contained within a unit mass of the liquid, excluding macro-level kinetic energy or potential potential energy of position.
Formula and Mathematical Derivation
The definition of enthalpy ($h$) serves as the primary gateway for determining specific internal energy. Enthalpy is formally defined as the sum of internal energy and the product of pressure ($P$) and specific volume ($v$):
$$h = u + P v$$To isolate the specific internal energy for a saturated liquid ($u_f$), we rearrange the fundamental enthalpy relation as follows:
$$u_f = h_f - P v_f$$Where:
- $u_f$: Specific internal energy of the saturated liquid ($\text{kJ/kg}$).
- $h_f$: Specific enthalpy of the saturated liquid ($\text{kJ/kg}$).
- $P$: Saturation pressure ($\text{kPa}$).
- $v_f$: Specific volume of the saturated liquid ($\text{m}^3/\text{kg}$).
The product $P \cdot v_f$ reflects the flow displacement work required to push the fluid into or out of a thermodynamic control volume. Since liquid phases are nearly incompressible, $v_f$ remains extremely small, making $P \cdot v_f$ a small fractional component relative to the magnitude of $h_f$.
How to Use This Calculator
Operating this computational tool requires three primary thermodynamic inputs extracted from experimental data or saturated fluid tables:
- Input Specific Enthalpy ($h_f$): Enter the known saturated liquid enthalpy in kilojoules per kilogram ($\text{kJ/kg}$).
- Input Saturation Pressure ($P$): Enter the equilibrium pressure corresponding to the saturation state in kilopascals ($\text{kPa}$).
- Input Specific Volume ($v_f$): Enter the specific volume of the liquid in cubic meters per kilogram ($\text{m}^3/\text{kg}$).
- Execute Calculation: Click the "Calculate Internal Energy" button. The software computes the flow work factor ($P \cdot v_f$) and subtracts it from $h_f$, dynamically displaying the output directly above the form area.