Energy Balance Fundamentals

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed. In engineering, we apply this principle using Energy Balances across a defined system boundary.

Closed Systems

A closed system can exchange heat and work with its surroundings, but no mass flows across its boundary. For a closed system undergoing a process from state 1 to state 2, the energy balance is:

(Note: The $Q - W$ sign convention assumes heat in is positive and work out is positive. Some textbooks use $Q + W$ by defining work as work done "on" the system. Always verify the sign convention.)

Often, changes in kinetic and potential energy in a closed system are negligible, simplifying the equation to $\Delta U = Q - W$.

Open Systems (Steady-Flow)

Open systems involve mass flowing across the system boundary (e.g., pumps, turbines, heat exchangers). For an open system at steady-state, the energy entering the system equals the energy leaving the system.

Because mass carries energy into and out of the system, we introduce Enthalpy ($H$), which combines internal energy and flow work ($U + PV$). The macroscopic steady-flow energy balance on a rate basis is:

Engineering Check

In the example above, a positive $\dot{W}_s$ confirms that 4 MW of power is produced by the system (turbine), which aligns with our chosen sign convention. If this were a compressor, $\dot{W}_s$ would be negative, indicating that work must be supplied to the system.