Engineering thermodynamics, steam plant & heat transfer

Thermodynamics & Heat Transfer

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Properties of State

L1
Lesson 1
Reading the state
pressure, temperature, heat — and which zero each one counts from
Thermodynamics is bookkeeping on a substance's state: the handful of numbers that say what condition it is in right now.
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L2
Lesson 2
Gauge versus absolute
one pressure, two zeros — and the gas laws accept only one of them
Every pressure gauge in the plant is lying to you, politely and by design. It has the atmosphere on both sides of its element, so the atmosphere cancels and the needle reads the EXCESS over ambient.
The formula in this lesson
$P_{abs} = P_{gauge} + P_{atm}$
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L3
Lesson 3
Heating a mass
The price of a degree, four ways round
Warming something costs energy, and every material charges its own rate.
The formula in this lesson
$Q = m c \Delta T$
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L4
Lesson 4
Changing phase
Where the thermometer stops and the bill begins
Heat a pot of ice and watch the thermometer. It climbs to 0 °C, then STOPS while the ice melts, then climbs again to 100 °C, then stops again while the water boils.
The formula in this lesson
$Q = m L$
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L5
Lesson 5
The gas laws
Boyle, Charles, Gay-Lussac — and the one law they are pieces of
Take a fixed amount of gas and move it from one state to another.
The formulas in this lesson
$P_1 V_1 = P_2 V_2$ , $\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}$ , $\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2}$ , $\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2}$
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L6
Lesson 6
The ideal gas
PV = nRT for any unknown, and a density from a molar mass
The gas laws compare two states of the same gas. The equation of state describes ONE state completely, and needs nothing to compare it to: PV = nRT, read aloud P V equals n R T.
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L7
Lesson 7
Real gas corrections
Z as the honest multiplier, and van der Waals as the reason for it
PV = nRT assumes two things that are not true: that molecules take up no room, and that they do not pull on one another.
The formulas in this lesson
$Z = \dfrac{PV}{nRT}$ , $\left(P + \dfrac{a n^{2}}{V^{2}}\right)\left(V - nb\right) = nRT$
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L8
Lesson 8
Vapour pressure curves
Antoine and Clausius–Clapeyron — why a vacuum boils water cold
Above every liquid sits its own vapour, pressing down with a pressure that depends on one thing only: temperature. When that vapour pressure reaches the pressure of the surroundings, the liquid boils.
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★
Boss lesson
The State Final
the boss · no calculator · one receiver heated, one deaerator duty
No calculator — the barometer reads a round 100 kPa, water costs a round 4 kJ/(kg·K), and steam a round 2250 kJ/kg.
The formula in this lesson
$P_{abs} = P_{gauge} + P_{atm}$
Start

Steam, Turbines & Power Cycles

L10
Lesson 10
Reading the steam table
saturation pressure and temperature, both directions
Everything in this chapter hangs off one curve: the saturation line, where water and steam sit together at the same temperature and pressure.
Start
L11
Lesson 11
Wet steam and quality
The h_g-for-h_fg mixup
Steam on the saturation line is rarely all vapour. Its quality x is the fraction of each kilogram that has actually boiled: x = 0 is saturated water, x = 1 is dry saturated steam, and a working header lives somewhere near 0.95.
The formulas in this lesson
$x = \dfrac{h - h_f}{h_{fg}}$ , $h = (1-x)\,h_f + x\,h_g$
Start
L12
Lesson 12
Degrees of superheat
how far above the line the steam is sitting
Keep heating dry saturated steam and it leaves the saturation line altogether.
The formula in this lesson
$\Delta T_{sh} = T - T_{sat}$
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L13
Lesson 13
Superheated enthalpy
h(p, T) · two coordinates to find the entry, one subtraction to use it
On the saturation line, pressure alone fixes everything: name the pressure and the table hands you the temperature and every enthalpy.
The formulas in this lesson
$h = h(p,\,T)$ , $q = h_2 - h_1$ , $\dot Q = \dot m\,(h_2 - h_1)$
Start
L14
Lesson 14
Flash steam
what boils off when condensate is let down
Hot condensate under pressure is holding more sensible heat than it can hold at a lower pressure. Open a trap into a flash vessel and the surplus goes somewhere: part of the water instantly boils.
Start
L15
Lesson 15
Turbine work
w = h₁ − h₂, and kJ/kg × kg/s = kW
Strip the steady-flow energy equation down to a turbine and almost everything cancels: no heat crosses the casing worth counting, and the velocity terms are small.
The formulas in this lesson
$P = \dot m\,w$ , $w = h_1 - h_2$
Start
L16
Lesson 16
Isentropic efficiency
the real drop against the drop the chart allows
A frictionless turbine would expand the steam at constant entropy and land at a specific point on the chart. A real one generates entropy, so it lands to the RIGHT of that point — higher enthalpy, less work extracted.
The formula in this lesson
$\eta_{isen} = \dfrac{h_1 - h_2}{h_1 - h_{2s}}$
Start
L17
Lesson 17
Steam losses and loads
leaks, spray water and condensate — the plant audit
Away from the turbine hall, steam engineering is bookkeeping. Three relations cover most of a plant walk-down, and all three are mass balances in disguise.
The formulas in this lesson
$\dot m = \dfrac{A\,P}{70}$ , $\dot m_w = \dot m_1\,\dfrac{h_1 - h_2}{h_2 - h_w}$ , $\dot m = \dfrac{\dot Q}{h_{fg}}$
Start
L18
Lesson 18
Cycle efficiencies
thermal, Carnot, Rankine, Otto, Brayton
Every efficiency on this page answers the same sentence — what you got, over what you paid for — and they differ only in what the question hands you.
The formulas in this lesson
$\eta = \dfrac{W}{Q_h}$ , $\eta = 1 - \dfrac{T_c}{T_h}$ , $\eta = \dfrac{(h_1 - h_2) - (h_4 - h_3)}{h_1 - h_4}$ , $\eta = 1 - \dfrac{1}{r^{\gamma - 1}}$
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Boss lesson
The Turbine Hall
the boss · no calculator · throttle to megawatts
Enthalpies are rounded to the nearest ten and the latent heat to a flat 2,400 kJ/kg — the kind of rounding an engineer does out loud on the machine floor, and the numbers are chosen to fit in your head.
The formula in this lesson
$x = \dfrac{h - h_f}{h_{fg}}$
Start

Conduction & the Building Envelope

L20
Lesson 20
Fourier's law
Thickness is the only thing fighting you
Heat does one thing in a solid: it walks from hot to cold, and it walks faster through some materials than others.
The formula in this lesson
$P = \dfrac{k A \Delta T}{d}$
Start
L21
Lesson 21
R-value of a layer
The number printed on the bag
Fourier's law is exact and inconvenient: nobody wants to carry a conductivity and a thickness around a job site.
The formulas in this lesson
$R = \dfrac{L}{k}$ , $R = \dfrac{L}{k A}$
Start
L22
Lesson 22
Stacking the wall
R-values in series · the air films count
A real wall is a sandwich: cladding, sheathing, insulation, a vapour control layer, gypsum, paint. Every watt that leaves the room crosses all of them, one after another, in a queue.
The formula in this lesson
$R_{tot} = R_1 + R_2 + R_3$
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L23
Lesson 23
From R to U
one clean reciprocal · and why U-factors never add
Insulation is sold in R-values; energy codes are written in U-factors.
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L24
Lesson 24
Whole-wall heat loss
design ΔT, real areas, and an estimate first
The two primes are the trade's way of writing “per unit area”. Flux is what a thermographer measures and what a designer compares between assemblies, because it does not care how big the wall is.
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L25
Lesson 25
The framing penalty
parallel paths · weight the U-factors, never the R-values
Every wall you have stacked so far pretended the insulation covered all of it.
The formula in this lesson
$\dfrac{1}{R_{eff}} = \dfrac{f_{fr}}{R_{fr}} + \dfrac{1 - f_{fr}}{R_{cav}}$
Start
L26
Lesson 26
Pipes and the critical radius
the log-mean geometry, and when lagging backfires
Everything so far assumed a flat wall: the same area at the hot face and the cold face. Wrap a pipe and that stops being true — the outside of the lagging has far more surface than the inside, and the heat spreads out as it crosses.
The formulas in this lesson
$\dot{Q} = \dfrac{2\pi k L \Delta T}{\ln(r_2/r_1)}$ , $r_{cr} = \dfrac{k}{h}$
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★
Boss lesson
The Envelope Audit
the boss · no calculator · films to flux, one wall
No calculator — every R-value in it sums to a clean number and every reciprocal is one you already know: RSI 2 is U-0.5, RSI 2.5 is U-0.4, RSI 4 is U-0.25, RSI 5 is U-0.2.
The formula in this lesson
$R_{tot} = R_1 + R_2 + R_3$
Start

Convection, Radiation & Heat Exchangers

L28
Lesson 28
Newton's law of cooling
The film coefficient, and the film as a resistance
Conduction happens inside solids. Convection happens where a solid meets a moving fluid, and almost all of the resistance lives in a thin, sluggish layer of fluid clinging to the surface — the boundary-layer film.
The formulas in this lesson
$\dot{Q} = h A \, \Delta T$ , $R = \dfrac{1}{hA}$
Start
L29
Lesson 29
The dimensionless crew
Re · Pr · Nu · Gr · Ra — which ratio is which
Nobody measures a film coefficient in the field. They correlate it — and every correlation is written in dimensionless groups, because a group that carries no units carries across scales, fluids and unit systems without being re-fitted.
Start
L30
Lesson 30
Dittus–Boelter
Nu from Re and Pr in turbulent tubes · then h
Read aloud: Nusselt equals nought-point-nought-two-three, Reynolds to the nought-point-eight, Prandtl to the n.
Start
L31
Lesson 31
Radiation exchange
εσAT⁴ · the fourth power demands kelvin
Every surface above absolute zero radiates.
The formulas in this lesson
$P = \varepsilon \sigma A T^{4}$ , $\dot{Q} = \varepsilon \sigma A (T_1^{4} - T_2^{4})$ , $h_t = h_c + h_r$
Start
L32
Lesson 32
Building the U
films plus wall in series · then foul it
An exchanger wall has fluid on both sides, so heat crosses three resistances in series: the inside film, the metal, the outside film.
The formulas in this lesson
$\dfrac{1}{U} = \dfrac{1}{h_i} + \dfrac{L}{k} + \dfrac{1}{h_o}$ , $\dfrac{1}{U_f} = \dfrac{1}{U_c} + R_f$
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L33
Lesson 33
Log mean temperature difference
pairing the ends · counterflow always wins
Along an exchanger, the gap between the two streams changes from one end to the other.
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L34
Lesson 34
Rating the exchanger
U·A·F·ΔT_lm against the stream balance
There are exactly two ways to say how much heat an exchanger moves, and a rating is honest only when both agree.
The formula in this lesson
$\dot{Q} = \dot{m} \, c_p \, \Delta T$
Start
L35
Lesson 35
Effectiveness–NTU
NTU · Cr · ε — rating without the outlets
The LMTD method needs all four terminal temperatures. Very often you know only the two inlets and the hardware — and then the effectiveness–NTU method is the one that works.
The formulas in this lesson
$\mathrm{NTU} = \dfrac{UA}{C_{min}}$ , $\dot{Q}_{max} = C_{min}\,(T_{h,in} - T_{c,in})$ , $\varepsilon = \dfrac{1 - e^{-\mathrm{NTU}(1 - C_r)}}{1 - C_r \, e^{-\mathrm{NTU}(1 - C_r)}}$
Start
L36
Lesson 36
Transient cooling
check Biot, then ride the lumped curve
A hot body dropped into cooler fluid has two resistances in series: conduction out through its own inside, and convection off its surface.
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★
Boss lesson
The Exchanger Final
the boss · no calculator · one unit, rated end to end
That last choice is a gift with a lesson inside it: with equal capacity rates in counterflow, the two streams' temperature profiles run parallel down the shell, both terminal differences come out identical, and the log mean quietly equals…
The formula in this lesson
$\dot{Q} = \dot{m} \, c_p \, \Delta T$
Start

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