Steady-State Energy Balances

Concept

An energy balance is an application of the First Law of Thermodynamics, which states that energy cannot be created or destroyed. For continuous chemical processes, we analyze open systems (control volumes) where mass flows across the boundaries. At steady state, the total energy entering the system equals the total energy leaving the system. For most process equipment (e.g., heaters, coolers, compressors), changes in kinetic and potential energy are negligible compared to heat and mechanical work terms. Thus, the energy balance revolves around Enthalpy ($H$), a property that combines internal energy and flow work.

Formula & Method

The general steady-state energy balance equation for an open system with one inlet and one outlet is:

Where $\Delta$ represents (outlet - inlet). If changes in kinetic energy ($\Delta E_k$) and potential energy ($\Delta E_p$) are neglected, the equation simplifies to:

For heat exchangers or vessels without moving parts, shaft work $W_s = 0$, leading to:

Engineering Meaning

Steady-state energy balances allow engineers to determine the utility requirements of a plant. Calculating $\dot{Q}$ helps engineers size the necessary boilers, furnaces, or cooling towers. Calculating $\dot{W}_s$ dictates the power required for compressors and pumps, or the power generated by turbines. Enthalpy is the crucial bridge linking mass flow rates to thermal demands.

Engineering Check

Always apply the sign convention for heat and work carefully. A common mistake is confusing work done on the system with work done by the system. Ensure that the specific enthalpy values used are referenced to the same thermodynamic reference state. When phase changes occur (e.g., boiling), remember that $h$ implicitly includes the latent heat of vaporization if pulled from a steam table.

Explicit Exclusions

This article only covers non-reactive energy balances. It does not cover energy balances in reacting systems (heat of reaction, heat of formation), transient energy balances, and entropy/exergy analysis.