SME
Material & Energy Balances
Energy balances
Use this for “How much steam at 100 °C warms 2 kg/s of water from 20 °C to 80 °C?”
Diagram
Energy in 668.8 = energy out 668.8 kW.
This is an example. Type your own values to start a new problem.
Q̇ (kW)
=
ṁ (kg/s)
×
cₚ (kJ/(kg·K))
×
(
Tₒᵤₜ (°C)
−
Tᵢₙ (°C)
)
ṁₛ (kg/s)
=
Q̇ (kW)
λ (kJ/kg)
Formulas
Q̇
=
ṁ
×
cₚ
×
(Tₒᵤₜ
−
Tᵢₙ)
501.6 = 2 × 4.18 × (80 − 20)
ṁₛ
=
Q̇
λ
0.2222
=
501.6
2,257
Assumptions
•
Steady open system; kinetic and potential energy changes are negligible.
•
Constant cₚ over the temperature range; the bar measures h = cpT from 0 °C.
•
The steam condenses fully and leaves as saturated liquid, giving up λ per kilogram.
•
Read λ = hfg from your steam table at the steam’s pressure: 2257 kJ/kg at 100 °C.
Step-by-step
WE KNOW
ṁ = 2 kg/s, cₚ = 4.18 kJ/(kg·K), Tᵢₙ = 20 °C, Tₒᵤₜ = 80 °C, λ = 2,257 kJ/kg
FIND
heat duty (Q̇), steam flow (ṁₛ)
Step 1 · Find heat duty (Q̇)
Use Q̇ = ṁ × cₚ × (Tₒᵤₜ − Tᵢₙ)
The energy balance on the water: the heat its warming takes.
Q̇
=
2
×
4.18
×
(80
−
20)
Q̇
=
2
×
4.18
×
60
Q̇
=
8.36
×
60
Q̇
=
501.6
kW
Step 2 · Find steam flow (ṁₛ)
Use ṁₛ = Q̇ ÷ λ
Each
kilogram
of
steam
that
condenses
gives
λ
.
ṁₛ
=
501.6
2,257
ṁₛ = 0.2222 kg/s
Check
Put the numbers back in. Both sides should match.
501.6 = 2 × 4.18 × (80 − 20) ✓
0.2222
=
501.6
2,257
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.