Chapter 2 · The Hero of Heat Transfer · Ten playable problems

Ch 2 · P1 — Three jobs at the wall

PROBLEM 11 · THE HERO OF HEAT TRANSFER — AT THE EXCHANGER WALL

At a heat exchanger, conduction, convection, and wetting each do one job moving heat into flowing water. Assign each job to the place it happens.

Live model

wall → film → flowPick a job, then click the place on the exchanger where it does its work.

Ch 2 · P2 — The shock absorber

PROBLEM 12 · THE HERO OF HEAT TRANSFER — SPECIFIC HEAT

Push the same heat into a pound of water and a pound of steel. The hydrogen bond network soaks up what the steel cannot.

Live model

ΔT = Q / (m × c)Add heat to both pounds. Same BTU in, very different climb.

Ch 2 · P3 — Two kinds of heat

PROBLEM 13 · THE HERO OF HEAT TRANSFER — THE HEATING CURVE

Follow one pound of water up the heating curve. Sensible heat moves the temperature; latent heat changes the phase. Click the stretch that is latent.

Live model

sensible moves the thermometer · latent moves the phaseDrag heat into the pound and watch the temperature stall. Then click the stretch that is latent heat.

Ch 2 · P4 — The boil under pressure

PROBLEM 14 · THE HERO OF HEAT TRANSFER — PRESSURE AND THE BOILING POINT

Why does raising the pressure raise the boiling point? Drag from deep vacuum to 250 psia, watch the boil chase the pressure, then click what actually sets it.

Live model

boiling: vapor pressure = surrounding pressureDrag the pressure. The boil follows it — then click what actually decides the boiling point.

Ch 2 · P5 — Dial in the climb

PROBLEM 15 · THE HERO OF HEAT TRANSFER — SENSIBLE HEAT CHAIN

Heat 500 gallons from 60°F to 180°F. Work the chain on paper, then dial the instrument to your answer in BTU.

Live model

Target 180°F

Q = m × c × ΔTWork the chain on paper: 500 gal × 8.34 lb/gal × 1 BTU/lb·°F × 120°F. Then dial the tank to your answer.

Ch 2 · P6 — Sensible against latent

PROBLEM 16 · THE HERO OF HEAT TRANSFER — ONE POUND, TWO HEATS

Heat one pound of water from 72°F to boiling, then vaporize it. Drag the heat in and watch which stretch is bigger.

Live model

140 BTU to reach the boil · 970 BTU to cross itStill climbing — every BTU shows on the thermometer.

Ch 2 · P7 — Heat into gallons

PROBLEM 17 · THE HERO OF HEAT TRANSFER — EVAPORATION RATE

A cooling tower rejects 6,000,000 BTU/hr. Dial the pounds it evaporates each hour until the heat balances, then read the gallons a minute.

Live model

1,000 BTU / lb · field value

lb/hr = BTU/hr ÷ 1,000 · gpm = lb/hr ÷ 8.34 ÷ 60The tower rejects 6,000,000 BTU/hr. Every pound evaporated carries a field value of 1,000 BTU away with it.

Ch 2 · P8 — The one percent rule, checked

PROBLEM 18 · THE HERO OF HEAT TRANSFER — RULE OF THUMB VS HEAT BALANCE

Estimate evaporation with the one percent rule on a 1,500 GPM loop at a 10°F range, then verify it through the heat balance.

Live model

a good rule of thumb survives the checkOne percent of the flow for every 10°F of range. Set your estimate, then check it against the heat balance.

Ch 2 · P9 — The price of a pound of steam

PROBLEM 19 · THE HERO OF HEAT TRANSFER — FEEDWATER TO STEAM

Feedwater enters at 50°F. Drag the heat in and find the sensible heat, the latent heat, and what a pound of steam costs in total.

Live model

(212 − 50) + 970 = 1,132 BTU/lbFeedwater climbing from 50°F. 0 of 162 sensible BTU in.

Ch 2 · P10 — Two properties, four systems

PROBLEM 20 · THE HERO OF HEAT TRANSFER — WHY WATER, EVERYWHERE

Water carries a high specific heat and a high latent heat of vaporization. Stamp each property on the systems that lean on it.

Live model

loops move temperature · boilers and towers move phasePick a property, then stamp it on every system that leans on it.

Problem set

The playable drawings need JavaScript. Every prompt and authored answer remains available below.

Problem 1
At a heat exchanger, what roles do conduction, convection, and wetting each play in transferring heat into flowing water?
Authored answer
Conduction transfers energy through the heat-exchanger wall and into the thin layer of water touching it. Convection carries the warmed water away and replaces it with cooler bulk water. Wetting helps maintain contact between the water and the surface, increasing the area available for conduction.
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Problem 2
The chapter describes the Hydrogen-Bond Network as a “molecular shock absorber.” In your own words, explain what this means and why it gives water a high specific heat.
Authored answer
Energy entering liquid water is distributed through molecular motion and continual rearrangement of the Hydrogen-Bond Network. Because the energy is spread across these modes rather than producing an immediate large increase in molecular speed, water’s temperature rises relatively slowly. That dampened response is the “shock absorber,” and it is the reason water’s specific heat is 1.0 BTU/lb·°F. Far higher than most common materials.
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Problem 3
What is the difference between sensible heat and latent heat? Which one changes temperature, and which one changes state?
Authored answer
Sensible heat changes temperature without changing phase; it increases the energy contained within the existing state. Latent heat changes state without substantially changing temperature.
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Problem 4
Why does raising pressure increase the temperature at which water boils? How does lowering pressure affect the boiling point?
Authored answer
Water boils when its vapor pressure equals the pressure surrounding it. At higher pressure, water must reach a higher temperature before vapor bubbles can form and survive. Lowering the surrounding pressure allows boiling to occur at a lower temperature.
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Problem 5
How many BTUs are required to heat 500 gallons of water from 60°F to 180°F? (Convert gallons to pounds first.)
Authored answer
500 gal × 8.34 lb/gal = 4,170 lb. Q = 4,170 lb × 1.0 BTU/lb·°F × (180 − 60)°F = 4,170 × 120 = 500,400 BTU.
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Problem 6
How much energy is required to (a) heat 1 pound of water from 72°F to 212°F, and (b) completely vaporize that same pound of water at 212°F? How many times more energy does vaporization require than heating the water from 72°F to 212°F?
Authored answer
(a) Sensible: 1 lb × 1.0 × (212 − 72) = 140 BTU. (b) Latent: 1 lb × 970 BTU/lb = 970 BTU. Vaporization requires 970/140 = 6.9 times more energy than heating to the boiling point.
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Problem 7
A cooling tower removes 6,000,000 BTU/hr. How many pounds of water must evaporate per hour? Assume that all heat is removed by evaporation and use a field latent-heat value of 1,000 BTU/lb. Convert to GPM.
Authored answer
6,000,000 BTU/hr ÷ 1,000 BTU/lb = 6,000 lb/hr. 6,000 lb/hr ÷ 8.34 lb/gal = 719.4 gal/hr ÷ 60 min/hr = 12.0 GPM.
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Problem 8
Using the 1% evaporation rule of thumb, a tower recirculates 1,500 GPM with a 10°F temperature drop. Estimate the evaporation rate in GPM. Then verify your answer using an idealized latent-only energy balance and 1,000 BTU/lb. (Q = m × cₚ × ΔT)
Authored answer
Rule of thumb: 1% of 1,500 GPM = 15 GPM evaporation for a 10°F drop. Verification: Q = 1,500 GPM × 8.34 lb/gal × 60 min/hr × 1.0 × 10°F = 7,506,000 BTU/hr. Evap = 7,506,000 ÷ 1,000 = 7,506 lb/hr ÷ 8.34 ÷ 60 = 15 GPM evaporation. The rule of thumb holds.
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Problem 9
A boiler produces steam at atmospheric pressure. The feedwater enters at 50°F. How many total BTUs per pound are required to produce steam? Break your answer into the sensible heat portion and the latent heat portion.
Authored answer
Sensible: 1 lb × 1.0 BTU/lb·°F × (212°F − 50°F) = 162 BTU. Latent: 970 BTU. Total: 162 + 970 = 1,132 BTU per pound of steam. Latent heat accounts for 86% of the total energy investment.
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Problem 10
Water has both a high specific heat and a high latent heat of vaporization. In 2–3 sentences, explain why these two properties make water useful in hot-water loops, chilled-water loops, boilers, and cooling towers.
Authored answer
Water’s high specific heat allows it to absorb and transport large thermal loads with relatively modest temperature changes, which makes it effective in hot-water and chilled-water loops. Its high latent heat allows a small mass of water to carry enormous amounts of energy during vaporization and condensation, which makes it effective in boilers and cooling towers.
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