PE Mechanical: HVAC and Refrigeration · Complete public sample

Open and closed system boundaries

Choose a batch-energy balance or a flow-energy balance from what crosses the boundary.

Understand the governing concept.

A closed system retains the selected mass while energy can cross its boundary. Heating a fixed batch of water therefore produces a finite energy change. An open control volume permits mass flow; at steady state, a heater must add energy at the rate carried by the moving water, with no accumulation.

Draw the boundary before naming an energy term. A thermal coil transfers heat across a water-only boundary; if the boundary instead encloses an electrical resistance element, electrical input is work crossing that boundary. State the sign convention and distinguish Btu from Btu per hour before comparing batch energy with equipment capacity.

By the end of this refresher

Explain the basis or assumption controlling this decision.
Apply the method within its stated limits.
Check the result and choose a related study task.

\Delta U=Q-W,\qquad \dot Q-\dot W=\dot m(h_2-h_1)

Q is heat into the selected system and W is work out. The flow relation is the one-inlet/one-outlet steady form with kinetic and potential changes neglected.

Define the basis before substituting a value
Symbol	Meaning	Unit or basis
$\Delta U$	Closed-system internal-energy change	Btu
$Q,W$	Heat into system and work out of system	Btu
$\dot Q,\dot W$	Heat-input and work-output rates	Btu/h
$\dot m$	Water mass flow for the rate equation	lb/h
$h$	Specific enthalpy	Btu/lb
$c$	Approximate liquid-water specific heat	Btu/(lb·°F)

When the method applies

The simplified water calculations use constant specific heat, negligible kinetic and potential energy changes, and negligible environmental heat loss.
For the batch, liquid internal-energy change is approximated by m c ΔT. For steady flow, liquid enthalpy change is approximated by c ΔT with pressure effects neglected.

Hydronic equipment illustrates water crossing a heat-transfer component boundary. — **Connect the physical model and the decision**Connect the equipment to the calculation

A sealed 40-lb batch is a closed system; a 4-lb-per-minute coil has mass crossing a steady control volume. Both have the same 40-degree-F temperature rise. — **Connect the physical model and the decision**Connect the equipment to the calculation

Original teaching case

Work the decision, then cross-check it.

Compare a sealed 40 lb water batch heated from 60°F to 100°F with water flowing steadily at 4 lb/min through a thermal heating coil over the same temperature rise. Use c = 1 Btu/(lb·°F); neglect losses, pressure effects, and shaft work.

For the closed batch, energy added is 40 × 1 × (100 − 60) = 1,600 Btu.
For the flow heater, heating rate is 4 × 1 × 40 = 160 Btu/min.
Convert the flow heating rate to hourly capacity: 160 × 60 = 9,600 Btu/h.

Q_{\mathrm{batch}}=1600\ \mathrm{Btu},\qquad\dot Q_{\mathrm{flow}}=9600\ \mathrm{Btu/h}

Decision

The batch requires an energy amount; the steady-flow heater requires a continuing heating rate. A batch-energy value cannot be used directly as an equipment-capacity value.

Independent check

In 10 min the flow heater processes 40 lb and adds 160 × 10 = 1,600 Btu, matching the batch mass and temperature rise.

A fresh application

Use the concept under changed conditions.

Choose a response before inspecting the reasoning. This is a learning check, separate from scored diagnostic and mock attempts.

Connect this refresher to your program.

Read the related E6 worked lesson →
Connect this prerequisite to the complete program explanation and its conditions.
Move to related program practice →
Use new questions after focused repair; keep learning checks separate from diagnostic and mock results.

The NCEES PE Mechanical Reference Handbook is the supplied examination reference. No separate design standards are listed for PE Mechanical: HVAC and Refrigeration. Refresh physical behavior, modeling choices and equation applicability alongside handbook navigation. This topic is classified as understanding and application; no individual reference omission has been verified.

Original ReasonSpan^™ teaching material. AI-assisted checks are complete; independent specialist review remains pending.