Energy Balance

Energy balances close the first law on a flowing system: heat added minus shaft work equals the change in enthalpy (plus small kinetic and potential terms), with all enthalpies referred to one common datum.

Key formulas & points

Skim these first — then read the full notes below.

  • Reference state for H must be consistent across streams
  • Adiabaticreactor:Q=0;isothermal:ΔT0withheatexchangeAdiabatic reactor: Q = 0; isothermal: \Delta T \approx 0 with heat exchange
  • Shaft work W_s is +ve when done ON system (Bhatt & Vora convention)

Topic details

Introduction

Following Bhatt & Vora, energy balances are always solved on top of a completed material balance because you need every stream flow before you can weight its enthalpy. You pick a reference temperature (often 25 °C), express each stream enthalpy as ṁCpΔT plus any latent or heat-of-reaction contribution, and then solve for the single unknown — usually the duty Q or an outlet temperature.

Key relations & formulas

QW=ΔH+ΔKE+ΔPEQ - W = \Delta H + \Delta KE + \Delta PE
(open system, steady flow)
ΔH=Σn˙outHoutΣn˙inHin\Delta H = Σ ṅ_out H_{out} - Σ ṅ_in H_{in}
(enthalpy flow terms)
Ws=VdPV˙ΔPW_{s} = \int V dP \approx V̇ \Delta P
(incompressible liquid pump work)

Notation and sign conventions

Relation 1 —
QW=ΔH+ΔKE+ΔPEQ - W = \Delta H + \Delta KE + \Delta PE
QW=ΔH+ΔKE+ΔPEQ - W = \Delta H + \Delta KE + \Delta PE
(open system, steady flow)
Write this relation with symbols exactly as in Stoichiometry — Bhatt & Vora before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
ΔH=Σn˙outHoutΣn˙inHin\Delta H = Σ ṅ_out H_{out} - Σ ṅ_in H_{in}
ΔH=Σn˙outHoutΣn˙inHin\Delta H = Σ ṅ_out H_{out} - Σ ṅ_in H_{in}
(enthalpy flow terms)
Write this relation with symbols exactly as in Stoichiometry — Bhatt & Vora before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
Ws=VdPV˙ΔPW_{s} = \int V dP \approx V̇ \Delta P
Ws=VdPV˙ΔPW_{s} = \int V dP \approx V̇ \Delta P
(incompressible liquid pump work)
Write this relation with symbols exactly as in Stoichiometry — Bhatt & Vora before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

The steady-flow energy equation is the accountant of heat and work. Kinetic and potential terms are usually negligible for process streams, so the working form is Q − Ws = ΔH. The subtlety is enthalpy bookkeeping: since only enthalpy differences matter, a consistent reference state must be used for all streams, and phase-change latent heats must be added when a stream crosses its saturation line. For reacting systems the standard heat of reaction at the reference temperature is added, letting you separate sensible-heat effects from chemical-energy effects (the Hess-law path).

Assumptions and validity limits

State assumptions explicitly before using any relation for energy balance — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Process Calculations viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Process Calculations papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to energy balance.
4. Use equation 1:
QW=ΔH+ΔKE+ΔPEQ - W = \Delta H + \Delta KE + \Delta PE
.
5. Use equation 2:
ΔH=Σn˙outHoutΣn˙inHin\Delta H = Σ ṅ_out H_{out} - Σ ṅ_in H_{in}
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Energy Balance appears in every chemical process design. In Indian chemical curricula this topic is tested because it connects theory to material and energy balances.
GATE and semester exams often combine energy balance with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use energy balance?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

The classic error is inconsistent reference states between inlet and outlet streams, which injects a spurious enthalpy. Others include ignoring latent heat when a stream vaporises, using Cp of the wrong phase, and getting the shaft-work sign backwards for a pump versus a turbine.

Quick revision checklist

Before attempting energy balance problems, confirm you can:
1. Reference state for H must be consistent across streams
2.
Adiabaticreactor:Q=0;isothermal:ΔT0withheatexchangeAdiabatic reactor: Q = 0; isothermal: \Delta T \approx 0 with heat exchange

3. Shaft work W_s is +ve when done ON system (Bhatt & Vora convention)
Revise the solved examples in Stoichiometry — Bhatt & Vora and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Heating a water stream

Problem

Water flows at 2 kg/s and is heated from 25 °C to 80 °C in a heat exchanger. With Cp = 4.18 kJ/kg·K, find the heat duty.

Solution

No shaft work, negligible KE/PE, so Q = ṁCpΔT = 2 × 4.18 × (80 − 25) = 459.8 kW. The positive sign confirms heat is added to the stream.

Conceptual check — Energy Balance

Problem

In a Process Calculations semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of energy balance." What should a complete answer include?

Exams & GATE

Combine with material balance — GATE often gives incomplete stream data.

📖 Standard books (India)

  • StoichiometryBhatt & Vora

    Read: Syllabus unit

    Process calculations for chemical engineering