CHE-33

Open-system energy balance

Q − W = m Cp ΔT for a single-stream heater (KE, PE dropped).

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BalancesFirst law

Governing equation

Q-W=\dot m c_p\Delta T

where

\dot m: Mass flow (kg/s)
c_p: Heat capacity (kJ/kg·K)
\Delta T: Temperature rise (K)
W: Shaft work out (kW)
Q: Heat in (kW)

Lecture brief

Historical brief

From CSTR/PFR mole balances and Arrhenius rates to McCabe–Thiele stages and NTU exchangers, chemical engineering is conservation plus equilibrium. The lab is that design arithmetic. This sheet (CHE-33 — Open-system energy balance) is the form associated with First law. Working symbols: $\dot m$ , $c_p$ , $\Delta T$ , $W$ $\rightarrow$ $Q$ . The steady-flow energy equation collapses to enthalpy when kinetic and potential changes are negligible. For an ideal liquid ΔH = Cp ΔT.

Purpose

Purpose: compute

Q

from

\dot m

c_p

\Delta T

W

in Chemical engineering via

Q-W=\dot m c_p\Delta T

Q − W = m Cp ΔT for a single-stream heater (KE, PE dropped). Use it when a real chemical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\dot m = 2.000\,\mathrm{kg/s}

c_p = 4.180\,\mathrm{kJ/kg·K}

\Delta T = 40.000\,\mathrm{K}

W = 0.000\,\mathrm{kW}

, the governing relation

Q-W=\dot m c_p\Delta T

yields

Q = 334.40\,\mathrm{kW}

. A heater, an inlet T, an outlet T, a Q arrow. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass flow \dot m2 kg/sHeat capacity c_p4.18 kJ/kg·KTemperature rise \Delta T40 KShaft work out W0 kW

Outputs

Heat in Q334.40 kW

Reading speed

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Narration of this film

A heater, an inlet T, an outlet T, a Q arrow.

The steady-flow energy equation collapses to enthalpy when kinetic and potential changes are negligible. For an ideal liquid ΔH = Cp ΔT.

Reading speed

Watch on YouTube