Energy balances, phase change and reacting processes

Heat, work and transported energy share one account

For steady flow with negligible changes in kinetic and potential energy, write heat into the boundary minus shaft work done by the system as the outlet enthalpy flow minus the inlet enthalpy flow. A mass flow multiplied by specific enthalpy has units of power. Enthalpy includes the flow-work contribution; do not add that contribution a second time.

Use consistent reference states for every stream and property. A stream’s enthalpy can depend on temperature, pressure, phase and composition. Constant heat capacity gives a useful sensible-enthalpy approximation over a stated range, but a phase change needs its latent contribution as well. The equation records an account; it does not guarantee that a proposed heat transfer is physically achievable.

An original hypothetical fluid illustrates the missing duty

Supply a 1 kg/s liquid inlet at 20 °C and a saturation temperature of 50 °C at the specified pressure. Assume constant liquid heat capacity 2 kJ/(kg K) and vaporisation enthalpy 300 kJ/kg. The outlet has 0.8 kg/s liquid and 0.2 kg/s vapour, both at 50 °C. These are invented properties for calculation, not water data.

Heating all the inlet liquid to 50 °C requires 1×2×30=60 kW. Vaporising 0.2 kg/s then requires 0.2×300=60 kW. With no shaft work, other losses or energy storage, total heat input is 120 kW. Counting only the temperature increase would omit half the required duty in this supplied example.

Chemical energy needs a declared convention

A reacting balance can use stream enthalpies that include standard formation enthalpies, or an equivalent reference method that separately includes reaction enthalpy and sensible contributions. Use one consistent method. Adding a reaction term to stream enthalpies that already account for the same chemical change counts that contribution twice.

For a separate constructed reaction at its reference conditions, let extent rate be 2 mol/s and reaction enthalpy be −40 kJ per mole of reaction as written. Their product is −80 kW. With unchanged sensible terms and no shaft work, heat into the boundary must be −80 kW: 80 kW leaves. Extent rate is an amount per time, and changing the written stoichiometric basis requires changing its corresponding enthalpy basis.

Check sign, units and exclusions

In the hypothetical phase-change case, 120 kJ/s equals 120 kW. Positive heat into the boundary matches the higher outlet enthalpy. If there were 10 kW of outward heat loss in addition to this desired stream change, a supplied heater would have to provide 130 kW under otherwise identical assumptions. The distinction is between net heat crossing the process boundary and a particular heater contribution.

The separate exothermic example instead needs heat removal to maintain its stated reference conditions. Neither result predicts transient temperature, heat-exchanger area or a reaction’s rate. Those questions need additional transport, property, kinetic and control information. A closed balance is necessary evidence about the account, not a complete thermal design.

Try the reasoning

1. Why is the phase-change duty 60 kW in the supplied example?

   Show the answer and reasoning

   Only 0.2 kg/s is vaporised, and 0.2×300 kJ/kg gives 60 kJ/s.

2. What does negative heat into the reacting boundary mean?

   Show the answer and reasoning

   Net heat leaves the boundary under the chosen sign convention.

3. Why must reaction enthalpy not be added indiscriminately?

   Show the answer and reasoning

   Stream formation-enthalpy accounting may already include the same chemical change, causing double counting.

What to carry forward

Keep phases, reference states, signs and chemical-energy conventions consistent before interpreting a process duty.