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Index/Chemical engineering/CHE-33

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=m˙cpΔTQ-W=\dot m c_p\Delta T

ΔT∈[−80,200]\Delta T \in \left[-80, 200\right]

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)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

CHE-33 · reactor
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①

Governing law — red

Q−W=m˙cpΔTQ-W=\dot m c_p\Delta T

ΔT∈[−80,200]\Delta T \in \left[-80, 200\right]

ΔT=−80\Delta T = -80Q=−668.8Q = -668.8

②

Domain of the variable — blue

ΔTmin⁡=−80,ΔTmax⁡=200\Delta T_{\min} = -80,\quad \Delta T_{\max} = 200

ΔT∈[−80,200]\Delta T \in \left[-80, 200\right]

ΔT=−80\Delta T = -80ΔT=−80\Delta T = -80

③

Response curve — green

Q−W=m˙cpΔTQ-W=\dot m c_p\Delta T

ΔT∈[−80,200]\Delta T \in \left[-80, 200\right]

ΔT=−80\Delta T = -80Q=−668.8Q = -668.8

④

Rate of change — amber

dQdΔT\frac{\mathrm{d}Q}{\mathrm{d}\Delta T}

ΔT∈[−80,200]\Delta T \in \left[-80, 200\right]

ΔT=−78.24\Delta T = -78.24Q′=8.36Q^{\prime} = 8.36

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: m˙\dot m, cpc_p, ΔT\Delta T, WW →\rightarrow QQ. 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 QQ from m˙\dot m, cpc_p, ΔT\Delta T, WW in Chemical engineering via Q−W=m˙cpΔTQ-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 m˙=2.000 kg/s\dot m = 2.000\,\mathrm{kg/s}, cp=4.180 kJ/kg⋅Kc_p = 4.180\,\mathrm{kJ/kg·K}, ΔT=40.000 K\Delta T = 40.000\,\mathrm{K}, W=0.000 kWW = 0.000\,\mathrm{kW}, the governing relation Q−W=m˙cpΔTQ-W=\dot m c_p\Delta T yields Q=334.40 kWQ = 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

Outputs

  • Heat in Q334.40 kW
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CHE-33 · reactor
00:0 / 00:08

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