Thermal Quiz 2

Heat (Q)

• heat is energy. It depends on how much material you have and how hot it is.

• Units: Btu (British thermal unit), joule (J), or calorie (cal).

temperature

measures the intensity of molecular motion (how hot or cold something is). Units: °F, °C, or K.

1 Btu =…

the energy needed to raise 1 lb of water by 1 °F.

which has more heat, a bathtub of ice water or a cup of hot coffee?

heat = (temperature above absolute zero) × mass

• Ice water: about 300 lb × 428 = 128,400 Btu.

• Hot coffee: about 0.5 lb × 630 = 315 Btu.

• Answer: the ice water has far more heat, even though the coffee has a much higher temperature. Heat depends on mass and temperature.

three forms of heat

sensible, latent, and radiant.

1st Law of Thermodynamics

energy is conserved. It can change form but cannot be created or destroyed

2nd Law of Thermodynamics

heat flows from the higher-temperature body to the lower-temperature body, until the two reach the same temperature.

4 heat transfer mechanisms

conduction, convection, radiation, and transport

conduction

energy transferred by direct contact between molecules (warm to cool). Example: your hand on a hot mug.

convection

energy transferred by fluid movement (air or water). Forced convection uses mechanical help like fans, and it increases the rate of heat transfer

radiation

energy transferred by electromagnetic waves through air or a vacuum. It needs a line of sight between surfaces. Everything above absolute zero radiates.

transport

heat moved by a carrier, such as ventilation air or hydronic (water) systems. Infiltration and exfiltration also move heat.

two kinds of radiation in buildings

solar and terrestrial

Solar radiation

• (shortwave)

• incoming from the sun (UV, visible, near infrared).

Terrestrial

•  (longwave, infrared)

• outgoing, emitted by all surfaces on earth.

heat flow always goes from…

warm to cold. Heat loss through the envelope happens by transmission, infiltration, and ventilation.

Transmission is…

the combination of conduction, convection, and radiation

the vacuum flask (thermos)

• Conduction: a vacuum gap (almost no air or material to conduct through) and supports that touch as little as possible.

• Convection: the vacuum means almost no air to circulate, so no convective loops.

• Radiation: the glass wall is coated with a reflective, low-emissivity layer that reflects heat back instead of passing it on.

• Thermal bridging: it occurs where solid parts connect inner and outer layers, such as the supports and the neck and lid area. Heat takes a shortcut there.

• Buildings are "just like a thermos." The Passive House Standard is a voluntary standard for ultra-low-energy buildings that need very little space heating or cooling, following the same logic.

Conductivity

• (k)

• a material's ability to conduct heat. Higher k means heat flows through faster (a worse insulator).

absorptivity

the fraction of incoming radiation a surface absorbs.

reflectivity

the fraction of incoming radiation a surface reflects.

transmissivity

the fraction of incoming radiation that passes through (think glass).

emissivity

how effectively a surface emits thermal radiation, on a scale of 0 to 1. Low-e surfaces (shiny metal coatings) emit little and make good radiant barriers.

Radiant barriers

a thin low-emissivity sheet can make as much difference as many inches of conventional insulation. They use the same technology developed from NASA's Echo satellite program. Use cases: a runner's foil blanket (keep heat in), an attic barrier (keep heat out).

Low-E windows

• Cold climates (heating-dominated): high-solar-gain low-E. It reduces heat loss but still admits solar gain. The coating is on the 4th (room-side) surface.

• Warm climates (cooling-dominated): low-solar-gain low-E (spectrally selective). It blocks solar heat but keeps visible light high. The coating is on the 2nd surface.

High conductivity examples

metals like copper, aluminum, steel (tens to hundreds of W/m·K). Concrete is moderate (around 1 to 2 W/m·K) and wood is low (about 0.1 to 0.15).

Heat flow rate (Q)

Q = U × A × ΔT

• Q = heat flow rate, in Btu/h

• U = U-factor, in Btu/(h·ft²·°F)

• A = area, in ft²

• ΔT = |T_inside − T_outside|, in °F

What makes Q go up?

A larger area, a larger temperature difference, or a higher U-factor (lower R-value).

What Q calculations are used for:

estimating energy use, comparing wall assemblies, checking code compliance (vs. a maximum allowable U-factor), and sizing mechanical systems.

Compactness (surface-to-volume ratio):

more envelope surface area for the same volume means more heat flow. Compact shapes lose less heat.

U-factor (thermal transmittance)

• Measures how easily heat passes through an assembly. Lower U = better.

• U = 1 / R_total (the reciprocal), and R_total = 1 / U.

• Defined as U = q / ΔT, where q is heat flux (rate per unit area). Note that q (flux) is not the same as Q (heat flow rate).

Compactness (surface-to-volume ratio):

 more envelope surface area for the same volume means more heat flow. Compact shapes lose less heat.

U envelope

• Σ(Uᵢ × Aᵢ) / ΣAᵢ

• Multiply each assembly's U by its area (walls, windows, roof, and so on), add them up, then divide by the total area.

Series

heat passes through layers one after another, so you add R-values.

Parallel

heat has side-by-side paths (through a stud or through the insulated cavity beside it), so you area-weight the U-factors.

Framing factor (FF)

the fraction of wall area taken up by framing. Formula: FF = stud width / stud spacing.

U total =

(FF × U_stud) + (1 − FF) × U_cavity

• FF matters because studs conduct much more heat than insulation. Ignoring them makes the wall look better than it is.

Thermal bridging

a path of higher conductivity (like a stud, a steel member, or a slab edge) that lets heat bypass the insulation.

why does thermal bridging matter?

• Why it matters: it reduces the effective R-value of the whole assembly.

• Fix: continuous insulation that wraps the outside of the structure without gaps. This is why exterior insulating sheathing is so effective.

thermal mass

• the ability of a material to absorb and store heat energy.

• acting like a "thermal battery" to smooth out indoor temperature swings

function of thermal mass in buildings

• Moderates (smooths out) indoor temperature swings.

• Reduces heat flow through the envelope.

• Stores energy.

• Reduces and shifts peak loads.

Q = TM × ΔT (Btu = Btu/°F × °F).

Energy stored = thermal mass × temperature change.

TM = SH × Mass

(thermal mass = specific heat × mass)

Mass =

Density × Volume

Specific heat (SH)

 heat needed to change a substance's temperature by a given amount, per unit mass. In IP: Btu/(lb·°F).

Volumetric heat capacity (VHC)

heat storage per unit volume, in Btu/(ft³·°F) in IP.

What thermal mass does to indoor temperature:

• Attenuates exterior temperature swings (the indoor swing is smaller).

• Delays the peak indoor temperature (time lag).

• More mass means a bigger effect.

Guidelines for effective use of thermal mass:

• There must be an adequate outdoor temperature swing (large day-to-night difference).

• Mass must be exposed to the indoor air.

• Mass must be well distributed.

• Mass must cycle continuously (it needs a chance to charge and discharge).

• Tradeoffs to remember: exposed finishes, acoustics, control issues and slow response time, weight and embodied carbon.

Passive heating with mass:

• Direct gain: sun enters through south-facing glass and hits a masonry floor or wall that stores the heat. Coordinate glazing, mass and sun path.

• Indirect gain (sunspace): a sunspace collects heat and passes it to the building. BedZED (south-facing sunspaces, no central heating) is the lecture example.

• South-facing glazing is best in the northern hemisphere, because the south facade gets the most solar gain in winter and the least in summer (apart from north).

Passive cooling with mass:

• Night-purge ventilation: concrete absorbs heat during the day (acts as a heat sink), and cool night air flushes the stored heat out. The mass sits inside the interior zone.

• Result: comfort without air conditioning.

• Ground coupling (e.g., NREL Research Support Facility) uses concrete as a big "thermal battery."

Climate analysis

for Phoenix, thermal mass and evaporative cooling work well in summer, and solar heating works well in winter. Thermal mass loves big daily temperature swings.

Sensible heat:

you can sense it. It changes the temperature (you can measure it with a thermometer). Example: a hot water storage tank.

Latent heat ("hidden")

energy absorbed or released during a change of state at constant temperature.

Heat of fusion

needed to melt a solid. Heat of vaporization: needed to turn a liquid into gas.

Numbers for 1 lb of water (from the lecture)

• Sensible: 1 Btu raises it 1 °F.

• Latent, melting: about 141 Btu to melt 1 lb of ice at 32 °F into water at 32 °F.

• Latent, evaporating: about 970 Btu to evaporate 1 lb of water.

• Takeaway: phase change absorbs far more energy than ordinary heating.

Phase change material (PCM):

• A substance with a high heat of fusion that stores and releases large amounts of energy by melting and solidifying at a certain temperature.

• Ice is the most common PCM.

• Building PCMs change phase within the human comfort range, about 20 to 30 °C.

• Below the melting point, a PCM acts like ordinary sensible storage. At the melting point, it absorbs lots of heat at almost constant temperature.

• Why this is good for buildings: PCMs store about 5 to 14 times more heat per unit volume than masonry or concrete.

PCM vs. conventional thermal mass:

PCM gives far more storage in a thin layer, but works only near its melting temperature. Conventional mass stores heat through temperature change (sensible heat).

The Four Control Layers: "The Perfect Wall"

Joseph Lstiburek's article argues that a good wall separates four jobs into four control layers, all placed on the exterior side of the structure.

Rain (water) control layer

keeps bulk water out. It is outermost because rain is the biggest moisture load. Includes cladding, a drainage gap, and the weather-resistive layer.

Air control layer

stops air leakage (infiltration and exfiltration). Air leaks carry heat and moisture, so this layer is critical for energy and durability.

Vapor control layer

limits water vapor diffusion, preventing condensation inside the wall.

Thermal control layer

 insulation. It slows conduction.

Why all outside the structure?

• The structure stays warmer and drier, so it lasts longer and is protected from temperature extremes and moisture.

• Exterior continuous insulation reduces thermal bridging through studs.

• It is simpler to build the layers in a continuous, uninterrupted way on the outside.

RVAT

from the outside in: Rain, Air, Vapor, Thermal.

Solar reflectance (albedo):

percentage of solar energy a surface reflects.

Thermal emittance

a surface's ability to shed heat as longwave (infrared) radiation.

Heat capacity:

urban materials have higher heat capacity than rural ones, so they store more heat.

Urban heat island (UHI)

dense urban areas can be more than 3.6 °F warmer at night than less-developed areas. Both areas receive about the same solar energy. The difference comes from how surfaces absorb and hold heat.

Cool roofs:

high solar reflectance + high emittance.

Green roofs:

in the Chicago example, the green roof surface was 91 to 119 °F vs. 169 °F for the dark conventional roof, and the air above it was about 7 °F cooler. Roofs make up about 20 to 25% of city land cover. Types: intensive and extensive.

Place de la République (Paris):

 reflective ground tiles, shade trees, water features for evaporative cooling, and leafless trees that let in winter sun.

U-factor

U = 1 / R_total, in Btu/(h·ft²·°F).

R-value

R in ft²·°F·h/Btu. R of a layer = thickness × R-per-inch.

Series layers

 R_total = R₁ + R₂ + … + Rₙ.

Parallel paths:

U_total = FF × U_stud + (1 − FF) × U_cavity.

Latent heat of water

about 141 Btu/lb to melt, 970 Btu/lb to evaporate.