Thermodynamics problems

Note: Beyond this entry page, all problems (except in Thermal radiation) are stated and solved in Spanish. Some exercises edited in English can be found within the Lectures.
I make extensive use (both in English and Spanish) of two Latin abbreviations: ‘i.e.’ for ‘which means’ (‘es decir’), and ‘e.g.’ for ‘for example’ (‘por ejemplo’).
Problems based on the book: I. Martínez, "Termodinámica básica y aplicada", Ed. Dossat, 1992, ISBN 84-237-0810-1. Although the book is out of print, much of the contents has been updated and placed on this web site. A list of equations of interest on thermal problems can be found aside (for Thermodynamics, and for Heat Transfer).
Problems (and simple exercises) are grouped in chapters corresponding to the book above and Lectures. The solutions presented below are not intended for teaching but for checking personal work (a solved problem is no longer a problem). The learning approach may be to choose a problem statement, try to apply the generic problem solving procedures you should know, and check your results with the solution here provided; iterate until you gain confidence on how to solve new problems (not until you have memorised a bunch of them).

The following information can be found on each problem:

See Problem tools and general layout for my apology for using the Maple tool, its constraints, and the rational applied to formulate and solve problems.

1 Energy (and introductory exercises with perfect gases and liquids)
2 Entropy
3 Exergy
4 Thermodynamic potentials and properties
5 Thermodynamics of control-volume systems
6 Thermodynamics of phase change
7 Thermodynamics of mixtures
8 Thermodynamics of humid air
9 Thermodynamics of chemical reactions
10 Thermodynamics of evolution
11 Thermal and mass diffusion
12 Thermal and mass convection
13 Thermal radiation
14 Other thermal and mass processes
15 Combustion processes: characteristics
16 Combustion processes: modelling
17 Thermodynamics of power generation
18 Thermodynamics of refrigeration and heat pumps
19 Energy management: resources and contamination
20 Design of thermal systems
21 Thermal metrology

Energy (and introductory exercises with perfect gases and liquids)

(Maple)Universal constants available
(Maple)Main equations
(Maple)Tabulated substance data
(Maple)Baby bath
(Maple)Cup of coffee
(Maple)Electric heater
(Maple)Hot tyre
(Maple)Standard atmosphere
(Maple)Solar collector
(Maple)Thermal capacity ratio
(Maple)Heat release with a piston
(Maple)Pushing a horizontal piston
(Maple)Trapped balloon
(Maple)Impact of a mass upon a piston
(Maple)Piston with a spring
(Maple)Piston oscillations
(Maple)Hydraulic actuator
(Maple)Rising a weight with heat
(Maple)Piston oscillations
(Maple)Piston forced and released
(Maple)Dewar flask
(Maple)Molar mass determination
(Maple)Flask with U-tube manometer

(Maple)Piston forced and released
((Maple)SCUBA Diving
(Maple)Diving bell

Maple)Quick opening of a bottle
(Maple)Temperature effect on floating bin
(Maple)Impact of a mass upon a piston
(Maple)Atmospheric changes in a gasmeter
(Maple)Galileo thermoscope
(Maple)Compression fire igniter
(Maple)Isentropic compression of a refrigerant gas
(Maple)Isentropic exponent of a gas
(Maple)Piston pushed and released
(Maple)U-tube manometer closed at one end (pdf)
(Maple)Cooking with solar energy
(Maple)Weighting the air (pdf)
(Maple)Heat and work in a cylinder-piston system
(Maple)Liquid column drop inside a capillary tube
(Maple)Trapped gas in a U-tube
(Maple)Galileo's thermoscope
(Maple,.ppt)Weight hanging from a piston
(Maple)Weight hanging from a piston (another)
(Maple)Pressure rise when closing with a stopper
(Maple)Weight release on a piston
(Maple)Sudden release of a piston


(Maple)Main equations
(Maple)Dice distribution
(Maple)Coins distribution
(Maple)Income distribution
(Maple)Molecular speed distribution
(Maple)Bar between thermal blocks (pdf)
(Maple)Clapeyron equation
(Maple)Maximum temperature in a system
(Maple)Piston forced and released
(Maple)Free expansion with vacuum
(Maple)Cylinder heating and piston release (vert.)
(Maple)Piston pushed and released
(Maple)Cylinder heating and piston release (horiz.)
(Maple)Piston pushed and released
(Maple)Piston loaded upside-down
(Maple)Closed cylinder with internal piston
(Maple)Quasi-static compression of ethylene
(Maple)Piston release with antagonic spring
(Maple)Piston push and release (.doc)


(Maple)Main equations
(Maple)Stirring heater
(Maple)Work from a body and a source
(Maple)Work from two bodies (pdf)
(Maple)Work from two sources
(Maple)Work for filling a compressed-air tank
(Maple)Work for a compressor
(Maple)Work from an unbalanced piston
(Maple)Minimum heating cost
(Maple)Lid blow

(Maple)Heat pump
(Maple)Making vacuum

(Maple)Energy and exergy comparison
(Maple)Work from a thermos bottle
(Maple)Compressed air car
(Maple)Pressure due to trapped dry ice
(Maple)Pneumatic energy storage for a mini-submarine
(Maple)Water heating with heat losses
(Maple)Geothermal power plant
(Maple)Nuclear power plant
(Maple)Comaparison of several space-heating plants
(Maple)Overall analysis of an absorption refrigerator
(Maple)Cogeneration: power, heating, cooling
(Maple)Piston displaced and released
(Maple)Minimum compression work in a control mass

Thermodynamic potentials and properties

(Maple)Main equations
(Maple)Mayer relation
(Maple)Maxwell relation
(Maple)Enthalpy potential
(Maple)Analysis of the h-s diagram
(Maple)Van der Waals reduced equation
(Maple)Dieterici reduced equation
(Maple)Redlich-Kwong reduced equation
(Maple)Berthelot reduced equation
(Maple)Analysis of the Molier chart
(Maple)Analysis of the p-h diagram
(Maple)Analysis of the T-s diagram
(Maple)Thermal expansion of water
(Maple)Compressibility corrections
(Maple)Analysis of the Z-pR diagram
(Maple)Flask with U-tube manometer
(Maple)Check of carbon dioxide p-h chart
(Maple)Check the entropy of water vapour
(Maple)Compression of R-134a

(Maple)Thermal expansion of rods
(Maple)Check of nitrogen p-h chart
(Maple)Quest on mercury data
(Maple)Sea-water model
(Maple)Analysis of Helmholtz potential

(Maple)Compatibility beteen v(T,p) and cp(T,p)
(Maple)Ballast tank in a submarine
(Maple)Sea-level rise due to global warming
(Maple)Identification by vapour-pressure data
(Maple)Checking glycol vapour-pressure data
(Maple)Alcohol thermometer design
(Maple)Cooling of an ammonia container
(Maple)Regasification of methane with seawater
(Maple)Cooling of a pressurised CO2 vessel
(Maple)Phase change data from vapour pressure data
(Maple)Volume of a two-phase system
(Maple)Liquid thermal expansion within a vessel
(Maple)Assembly by thermal expansion
(Maple)Thermal expansion of railways
(Maple)Thermal expansion of cryogenic sensor
(Maple)Thermal expansion of heavy water
(Maple)CO2 fire extinguisher
(Maple)Thermal sag in a catenary
(Maple)Mass content of methane and ethane bottles
(Maple)Estate of a given mass in a given volume
(Maple)Cooling down of a steam pressure-vessel
(Maple)Cooling down of a propylene vessel
(Maple)Thermalisation of a cold CO2 vessel
(Maple)Analytical compressibility corrections for SO2
(Maple,.doc)Thermalisation of a methane vessel

Thermodynamics of control-volume systems

(Maple)Main equations
(Maple)Quick opening of a bottle
(Maple)Heating an open room
(Maple)Sudden filling of an evacuated flask
(Maple)Compressed air turbine
(Maple)Stirrer in an open room
(Maple)Effect of pressure on internal energy
(Maple)Heating in a two-flask connection
(Maple)Diverging nozzle
(Maple)Natural convection loop
(Maple)Pumping water into an air-tight tank
(Maple)Loading a pneumatic accumulator
(Maple)Cost of vapour making
(Maple)Loading a compressed-air tank
(Maple)Volumetric compressor
(Maple)Compression with intercooling
(Maple)Force to open a refrigerator
(Maple)Cost of compressed-air making
(Maple)Work from compressed-air
(Maple)Cost of compressing ethane
(Maple)Hair-dresser heater
(Maple)Geothermal source

(Maple)Volumetric compressor
(Maple)Work from a compressed-air tank
(Maple)Work from a compressed-air line

(Maple)Filling ethane bottles
(Maple)Lifting a sea-bed object
(Maple)Compressed-air explosion

(Maple)Connecting two air-tanks
(Maple)Filling carbon-dioxide bottles
(Maple)Work from a fluid line
(Maple)Fluid actuator
(Maple)Heating an air tank with valve
(Maple)Supply from a butane bottle
(Maple)Stock of compressed-air bottles
(Maple)Compressed-air intake from a line
(Maple)Argon throttling
(Maple)Sonic vapour nozzle
(Maple)Air filling in a cylinder-piston
(Maple)Compressed air for engine start-up
(Maple)Speed measurement in a vapour line
(Maple)Entropy check in a mixing chamber
(Maple)Entropy check in a mixing chamber
(Maple)Solar chimney
(Maple)Two-stage turbine with reheating
(Maple)Heating one of two connected vessels
(Maple)Exergy analysis of a Ranque tube
(Maple)Air ejector
(Maple)Maximum work output from two air streams
(Maple)Isentropic expansion to saturated vapour state
(Maple)CO2 compression
(Maple)CH4 compression
(Maple)Heating in a two-flask connection(.doc)

Thermodynamics of phase change

(Maple)Main equations
(Maple)Basic functions and procedures
(Maple)Heating a tank
(Maple)Level change with heating
(Maple)Filling a tank
(Maple)Throttling propane
(Maple)Release valve
(Maple)Geothermal source
(Maple)Hanging piston
(Maple)Heat pumping to a tank
(Maple)Peabody meter
(Maple)Mixing chamber
(Maple)Isentropic expansion
(Maple)Heating a supply tank
(Maple)Throttling ethylene 
(Maple)Two states of acetylene
(Maple)Condensing propylene line
(Maple)Self-cooling tank (pdf)
(Maple)Filling ethane bottles
(Maple)Throttling ethylene
(Maple)Venting cryogenic fluid
(Maple)Expansion with ethylene
(Maple)Heating a supply bottle
(Maple)Pushing a piston by heat
(Maple)Piston release
(Maple)Rocket propulsion
(Maple)Filling from a bottle manifold
(Maple)Release valve
(Maple)Mixing chamber
(Maple)Piston on supports
(Maple)Water vacuum
(Maple)Solid-liquid equilibrium
(Maple)Hot-water tank expansion

(Maple)Bottle immersion in a tank
(Maple)Release from a flask
(Maple)Piston release
(Maple)Piston between two systems

(Maple)Isentropic expansion
(Maple)Turbine expansion
(Maple)Vapour pressure curve fitting
(Maple)Torricelli's experiment
(Maple)Air-vacuum by boiling
(Maple)Heat pump with R-134a
(Maple)Making vacuum
(Maple)Filling a flask with NH3
(Maple)Making vacuum in a dewar
(Maple)Bubbling benzene over mercury
(Maple)Damage caused by tank explosion
(Maple)Butane bottle magnitudes
(Maple)Pressure cooker model
(Maple)Small vapour generator
(Maple)Vapour cleaner
(Maple)Liquid nitrogen engine
(Maple)Butane compression and cooling
(Maple)CO2 usage on draft beer
(Maple)Vapour extraction from a two-phase vessel
(Maple)Lighter re-charger
(Maple)Liquid ice production by vacuum
(Maple)Cooling down of steam at constant volume
(Maple)LNG regasification plant
(Maple)Geothermal power with flash chamber
(Maple)Dual-fuel engine using LNG
(Maple)Control volume processes with R134a
(Maple)Steam ejector
(Maple)Small steam generator
(Maple)R134a condenser
(Maple)Water boiler driven by oxy-combustion gases
(Maple)CO2 supply from a bottle
(Maple)Peabody meter

Thermodynamics of mixtures

(Maple)Main equations
(Maple)Cost of air demixing (pdf)
(Maple)Uranium enrichment
(Maple)Heavy water separation
(Maple)Liquid air composition (pdf)
(Maple)Natural gas composition
(Maple)Propane-butane mixture
(Maple)Butane bottle (pdf)
(Maple)Molar mass by osmosis
(Maple)Cryoscopic descent
(Maple)Entropy of mixing
(Maple)CO2 discharge in a room
(Maple)Two-system partition release
(Maple)Air composition variation (pdf)
(Maple)Effect of weight on composition
(Maple)Heating with exhaust gasses
(Maple)Colloidal segregation
(Maple)Exhaust gas composition
(Maple)Propane-butane mixtures
(Maple)Gas intake

(Maple)Colloidal segregation
(Maple)Two-system partition release
(Maple)Dry ice into a bottle

(Maple)Properties of an exhaust jet
(Maple)Two-phase enthalpy and density
(Maple)Purge in a cooling tower

(Maple)Injecting propane in a butane reservoir
(Maple)Separation of a two-phase mixture
(Maple)Boiling-off in a natural gas reservoir
(Maple)Flash expansion of a liquid mixture
(Maple)Gas exchange in a large tank
(Maple)Mixing entropy
(Maple)Boiling temperature of ethanol-methanol mixtures
(Maple)Water heating with exhaust gases
(Maple)Two phase state of a propane-ethane mixture
(Maple)Oxygwn injextion in a bomb calorimeter
(Maple)Carbon dioxide/hydrogen mixture
(Maple)Preparation of a gas mixture
(Maple)Gas mixture through a turbine and nozzle
(Maple)Two-phase mixture in a given volume
(Maple)Adiabatic expansion with condensation
(Maple)Cold gas rocket
(Maple)Vapour fraction in a propane-butane bottle
(Maple)Gas sample from a propane-butane bottle
(Maple)Must and wine densities
(Maple)Gas mixture in a cylinder-piston system
(Maple)Compression of a propane-air mixture
(Maple)Discharge from an O2-tank to a N2-tank
(Maple)Boil-off from a LNG with 1 % N2
(Maple)Ar/O2 mix for Joule-Thomson cooler
(Maple)Connecting two gas tanks with different pressure
(Maple)Air entering a vessel holding water vapour
(Maple)Liquid flashing from a propane/butane vessel
(Maple)Atmosphere in Titan moon
(Maple)Exergy of two streams mixing
(Maple)CO2 capture from exhaust gases
(Maple)Exergy of air separation
(Maple)An argon/xenon mixture for a space engine

Thermodynamics of humid air

(Maple)Main equations
(Maple)Ambient air
(Maple)Heating a two-phase system
(Maple)Humidity change on compression
(Maple)Adding vapour to air
(Maple)Condensation by compression (pdf)
(Maple)Exergy of a tank
(Maple)Refrigeration of a power station
(Maple)Wet tower
(Maple)Summer air-conditioning
(Maple)Wet tower
(Maple)Wet tower
(Maple)Summer air conditioning
(Maple)Water intake in a tank
(Maple)Vapour addition
(Maple)Water addition
(Maple)Water intake in a tank
(Maple)Heating a two-phase system
(Maple)Heating a two-phase system
(Maple)Cooling humid air
(Maple)Cloth dryer
(Maple)Mixing chambers
(Maple)Mixing with hot vapour

(Maple)Vapour tank discharge in air
(Maple)Mixing chamber
(Maple)Evaporative cooling
(Maple)Mixing with vapour
(Maple)Exhalation mist

(Maple)Ambient air
(Maple)Mixing chamber
(Maple)Humidifying natural gas

(Maple)Exergy of humid air

(Maple)Exhaust from a submarine engine
(Maple)Mist by suddent air expansion

(Maple)Malt drying with a heat pump
(Maple)The model water-nitrogen
(Maple)Vapour addution with oversaturation (pdf)
(Maple)Thermal capacity in saturation
(Maple)Adding cold water to air
(Maple)Nitrogen and water equilibrium
(Maple)Cooling tower
(Maple)Vapour injection in an air stream
(Maple)Submerged test-tube with air and water
(Maple)Preparation of humidified air for a fuel cell
(Maple)Humidification with saturated vapour (pdf)
(Maple)Making ice by evaporative cooling with dry air
(Maple)Cooling tower for 1 MW
(Maple)Dew point on compression and expansion
(Maple)Air conditioning with bypass
(Maple)Air conditioning with bypass
(Maple)Cooling tower
(Maple)Sudden expansion in a saturated vessel
(Maple)Water-vapour contents of Earth atmosphere
(Maple)Cooling tower with purge
(Maple)Dehumidification of an air stream
(Maple)Air conditioning with mixing
(Maple)Water with CO2
(Maple)Drying with heated air
(Maple)Air conditioning with mixing
(Maple)Aircraft air conditioning
(Maple)Heating an air stream with hot steam
(Maple)Cooling tower with draining
(Maple)Mixing an air stream with a larger water stream
(Maple)Closed circuit clothes dryer
(Maple)Air compression with evaporative cooling
(Maple)Air condensation in a vacuum chamber
(Maple)Italian coffee maker
(Maple)Vacuum bell with air infiltration
(Maple)Dryer with heat pump
(Maple)Sea water desalation by air dehumidification
(Maple)Air conditioning with dehumidification wheel
(Maple)Indirect evaporative cooling
(Maple)Air humidification with water and steam
(Maple)Relative humidity change during air expansion
(Maple)Adiabatic mixing of air and water

Thermodynamics of chemical reactions

(Maple)Nomenclature and basic procedures
(Maple)Main equations
(Maple)Vapour and air over coal bed
(Maple)Enthalpy of ethane
(Maple)Liquid-vapour equilibrium
(Maple)Graphite-diamond equilibrium
(Maple)Enthalpy of hydrazine
(Maple)NH3 production
(Maple)CO2 dissociation (pdf)
(Maple)CO2-CO equilibrium
(Maple)Water gas production
(Maple)Water gas equilibrium
(Maple)CO2-CO equilibrium
(Maple)Air dissociation
(Maple)Town gas manufacture
(Maple)Electromotive force
(Maple)Methanol production
(Maple)Propane combustion
(Maple)Equilibrium composition
(Maple)CO combustion

(Maple)TNT explosion in a tank
(Maple)Methanol production
(Maple)Thermochemical data check (pdf)

(Maple)Exergy of fuels
(Maple)Gibbs-Duhem equation
(Maple)CO combustion

(Maple)NO reduction by NH3
(Maple)Gasoline injection in a vessel
(Maple)Exergy of hydrogen combustion
(Maple)Exergy of water electrolysis
(Maple)Natural gas reforming
(Maple)Natural gas reforming
(Maple)Natural gas pyrolysis
(Maple)Linearity of equilibrium constant versus 1/T
(Maple)Vacuum generated by water condensation
(Maple)Hydrogen reaction with carbon dioxide
(Maple)Bomb calorimeter calibration
(Maple)Catalytic craking of Jet A-1
(Maple)Catalytic craking of Jet A-1
(Maple)Glucose test in a bomb calorimeter
(Maple)Hydrazine rocket
(Maple)Town gas (pdf)
(Maple)Liquid propellants in a rocket
(Maple)Air revitalisation in a space station
(Maple)Nitrocellulose-nitroglycerine propellant
(Maple)Hydrazine use in a Martian novel
(Maple)UDMH and NTO for space propulsion
(Maple)Kerosene and nitric acid rocket
(Maple)Kerosene and NTO rocket
(Maple)Aluminium powder for auxilliar power unit
(Maple)Ethanol reforming
(Maple)Black powder rocket
(Maple)Energy density of aluminium
(Maple)Adiabatic decomposition of liquid N2O
(Maple)Thermochemical exhaust heat recovery
(Maple)Stoichiometric combustion of H2 and O2

Thermodynamics of evolution


Thermal and mass diffusion

(Maple)Main equations
(Maple)Planar compound wall
(Maple)Planar compound wall (ship cargo hold)
(Maple)Cylinder with internal heat sources
(Maple)Shaft friction
(Maple)Simple fin
(Maple)Rod touching boiling oil
(Maple)Simple clothing model
(Maple)Furnace with periodic heating
(Maple)Joule dissipation in a wire
(Maple)LNG tank insulation
(Maple)Wall suddenly exposed to sun radiation
(Maple)Thermal run away
(Maple)Nuclear fuel rod
(Maple)Water freezing by air changing temperatures
(Maple)Air gap between pot and cooker
(Maple)Downstream cooling of hot water in a pipe
(Maple)Alcohol drop evaporation
(Maple)Loschmidt cell
(Maple)Rod with end heat sources
(Maple)Semiinfinite rod
(Maple)Electrical wire
(Maple)Rod with unsymmetric end sources
(Maple)Glass window with frame
(Maple)Self-heating rod with cooled ends
(Maple)Partially immersed stem
(Maple)Hemispherical rod (handle)
(Maple)Liquid nitrogen spherical vessel
(Maple)Rod with internal sources
(Maple)Evaporation of a water droplet
(Maple)Sudden heating of a slab

(Maple)Freezing of a water layer (Stefan's problem)
(Maple)Partially insulated rod
(Maple)Water pipe with heat sources in the wall
(Maple)Prescribed temperature profile in a rod
(Maple)Principal solutions to the heat equation
(Maple)Unsteady diffusion within a wall
(Maple)Constrains in temperature profiles
(Maple)Constrains in a given temperature profile
(Maple)Finned pipe in a bus heating system

(Maple)Car rear window defrosting
(Maple)Spherical vessel with liquid oxygen
(Maple)Chip cooling fan
(Maple)Electrical conductor with insulation
(Maple)Rod between boiling water and ice

(Maple)Sphere and shell with dissipation
(Maple)Cooling drinks in an ice box

(Maple)Hot water cooling in a glass
(Maple)An old ice box

(Maple)Test tube partially immersed in boiling water
(Maple)Rod with partial insulation
(Maple)Conical support
(Maple)Walking bare-foot on hot sand
(Maple)Thin steel plate with icy ends
(Maple)Cooling an electronics plug-in card
(Maple)Mass diffusion through a rubber wall
(Maple)Droplet evaporation in a very hot environment
(Maple)CO2 bubble dissolving in water

(Maple)Thermal conductivity of a sample
(Maple)Effect of solar irradiation on a wood slab
(Maple)Solving a fin problem by yuxtaposition
(Maple)Sudden end-temperature change in a copper sheet
(Maple)Metal rod with a cork sheath
(Maple)Temperature of a cane shadow-cover
(Maple)Thermal conductivity hot-wire probe
(Maple)Joule heating of a wire with insulation
(Maple)Thermal relaxation of an iron plate
(Maple)Oscillating heat transfer in an engine wall (pdf)
(Maple)Symmetric bar
(Maple)Putting a slab into boiling water
(Maple)Unsymmetric point-heating in a bar
(Maple)A rod in air with mixed boundary conditions
(Maple)Rear window heater
(Maple)A wall with insolation
(Maple)Satellite platform with embedded battery (pdf)
(Maple)Dew on double pane window (pdf)
(Maple)Thermal transients in a CFRP wall (pdf)
(Maple)Floor heating in a room

(Maple)Adiabatic relaxation from a steady state
(Maple)Kelvin's estimation of age of the Earth
(Maple)Iced ball immersed in boiling water
(Maple)Printed circuit board with time-varying dissipation
(Maple)Printed circuit board with dissipation in two strips
(Maple)Printed circuit board with two large integrated circuits (pdf)

(Maple)Printed circuit board with central dissipation (pdf)
(Maple)Printed circuit board with highly conductive dielectric

(Maple)Rod with a dissipating sphere at one end
(Maple)LOX tank in space
(Maple)LPG tank underground
(Maple)Ablation in a steel plate
(Maple)Aircraft cabin insulation
(Maple)Kapton heater between plates
(Maple)A wood on water at noon
(Maple)Bended plate in geostationary orbit
(Maple)Radiator with heat-pipe condenser
(Maple)Printed circuit board with central dissipation
(Maple)Box with internal dissipation (pdf)
(Maple)Box with internal dissipation and its radiator

(Maple)Spacecraft outer wall with ribs
(Maple)Printed circuit board with three IC

Thermal and mass convection

(Maple)Refrigerant vapour superheating
(Maple)Heating of a variable properties viscous oil
(Maple)Heat losses in a steam pipe
(Maple)Natural cooling of a hot ball in air
(Maple)Producing hot water with an electrical heater
(Maple)Steam condenser of given transfer area
(Maple)Forced air cooling of a hot thin flat plate

(Maple)Number of tubes in a steam condenser
(Maple)Droplet evaporation in an air stream
(Maple)Kerosene cooling
(Maple)Water-to-water heat exchanger
(Maple)Temperature profiles in water pipe flow
(Maple)Temperature profiles in oil pipe flow
(Maple)Oil cooling in a tubular heat exchanger
(Maple)Heat recovery from waste hot water
(Maple)Heating water in a pipe
(Maple)Insulating an air conditioning duct
(Maple)Electrical water heater
(Maple)Steam condenser
(Maple)Plate heat exchanger for heat recovery
(Maple)Entry length and temperature profiles
(Maple)Water-water heat recovery

Thermal radiation

(Maple)Light bulb filament emission
(Maple)Fraction of blackbody emission visible
(Maple)Effect of radiation on thermocouple reading
(Maple)Cylindrical solar collector
(Maple)Radiative shields
(Maple)Radiative effects on rocket fuel tank
(Maple)Planar solar collector
(Maple)Sun temperature
(Maple)Ground temperature
(Maple)Greenhouse filter
(Maple)Spherical shell in space
(Maple)Spherical shell with semi-transparent coating
(Maple)Earth temperature as a sphere in space
(Maple)Effect of the Earth on a GEO radiator
(Maple)Heat loss in a second surface radiator in space
(Maple)Steady temperature for a sphere in a room
(Maple)Radiation from a 100 W light bulb
(Maple)Comparison of convective and radiative losses
(Maple)Planck’s law corollaries
(Maple)Solar time vs. regular time: time equation
(Maple)Solar constant measurement from ground
(Maple)Earth thermal loads vs. altitude
(Maple)Moon emissivity from albedo
(Maple)Thermal balance of a plate in Martian orbit (pdf)

(Maple)Thermal balance of a plate in LEO
(Maple)Heater manufacturer data
(Maple)View factor from patch to disc
(Maple)View factor from hemisphere to smaller disc

(Maple)View factors and heat exchange in a cubic box
(Maple)View factors in a cubic box with a heated face
(Maple)Radiation exchange inside a triangular pole

(Maple)View factors and thermal balance in a cylinder
(Maple)Solar irradiance and steady temperature vs. distance
(Maple)Energy balance in LEO and GEO with eclipse. Sphere

(Maple)Energy balance in LEO and GEO with eclipse, Cube
(Maple)Steady temperature at 1 AU. Effect of alpha/epsilon

(Maple)Solar cell effect on thermal balance
(Maple)Steady temperature at 1 AU. Effect of geometry
(Maple)Two nodes model: a disc and a sphere

(Maple)Two nodes model: two grey discs
(Maple)Two nodes model: two blackbody discs
(Maple)Sleeve cooling down
(Maple)Lit grove in air
(Maple)Lit grove in space
(Maple)Hemispherical hollow body lit from its side
(Maple)Two perpendicular plates not touching
(Maple)Hemispherical hollow body lit from its face
(Maple)Hemispherical hollow body lit from its face (bis)
(Maple)Steel strip perpendicular to large plate in vacuum
(Maple)White fin normal to a white plate (pdf)
(Maple)Solar panel with honeycomb structure (pdf)
(Maple)Refrigerated display case
(Maple)Temperature of desert sand at midday
(Maple)Spherical shield outside an sphere
(Maple)Disc shield protecting a spherical probe near the Sun
(Maple)Twin-tube appendix in a geostationary orbit
(Maple)Two grey discs in a vacuum chamber
(Maple)Two parallel square plates in GEO (pdf)
(Maple)Two parallel equal discs in GEO

(Maple)Sphere with grey hemisphere in a vacuum chamber (pdf)
(Maple)Two equal perpendicular plates not touching (pdf)
(Maple)Cylindrical enclosure with a base facing CBR

(Maple)Two unequal parallel discs with complementing ring
(Maple)Thermal balance of a black and a white ball
(Maple)Spherical appendage in GEO at equinox
(Maple)Spherical shell close to the Sun
(Maple)Detached radiator sizing
(Maple)Two parallel hemi-cylinder strips in GEO (pdf)
(Maple)Stratospheric balloon (pdf)

(Maple)Bended plate in geostationary orbit
(Maple)Venusian satellitte (pdf)
(Maple)Spherical satellite in LEO

(Maple)Small sphere in LEO at terminator
(Maple)Two parallel grey discs in halo orbit
(Maple)Hollow box with sun at the edge
(Maple)Hollow box with sun normal to a face
(Maple)Liquid hydrogen tank with a sunshield
(Maple)Hollow box with sun at the vertex
(Maple)Hollow sphere in LEO

Other thermal and mass processes


Combustion processes: characteristics

(Maple)Nomenclature and basic procedures
(Maple)Nomenclature and basic procedures
(Maple)Main equations
(Maple)Fuel & components heating values
(Maple)Constant volume heating value
(Maple)Theoretical air for octane
(Maple)Ignition limit of a fuel mixture
(Maple)Dry basis analysis of flue gas
(Maple)Petrol engine exhaust
(Maple)Excess of air approximation
(Maple)Finding a fuel composition
(Maple)Amount of condensate
(Maple)Heat output and dry analysis
(Maple)Combustion efficiency in a gas turbine
(Maple)Methane adiabatic flame temperature
(Maple)Octane adiabatic flame temperature
(Maple)Theoretical air for a coal
(Maple)Exergy efficiency of cambustion
(Maple)Wood gas generation
(Maple)Gas turbine with kerosene
(Maple)Burning butane with humid air
(Maple)Anaerobic digestor
(Maple)Excess of air approximation
(Maple)Burning acethylene
(Maple)Analysis of a coal
(Maple)Dew point of flue gas
(Maple)Burning ethane in air
(Maple)Water addition with propylene
(Maple)Drop burning in a vessel

(Maple)Butane/air in an spherical vessel
(Maple)Camping-gas bottle hazards
(Maple)Gas turbine with octane
(Maple)Find the fuel from exhaust analysis
(Maple)Premixed flame burner
(Maple)Water addition with dodecane

(Maple)Water addition with octane
(Maple)Heating loads in a hall
(Maple)Oxides formation in a gas turbine
(Maple)Exhaust temperature
(Maple)Fuel estimation for a boiler

(Maple)Fuel estimation for a gas turbine
(Maple)Checking human metabolic rate
(Maple)Product of ethylene combustion
(Maple)Changing the type of fuel gas

(Maple)Fuel estimation for a boiler
(Maple)Fuel cell for a car (pdf)
(Maple)Drying wood by burning a fraction of it
(Maple)Hydrogen combustion in a vessel
(Maple)ICE exhaust energy losses
(Maple)Rich combustion emissions (n-octane)
(Maple)Rich combustion emissions (methane)
(Maple)Density of product gases
(Maple)Combustion flow calorimetre
(Maple)Volta eudimeter
(Maple)Inert gas generation
(Maple)Wood dryer
(Maple)Sealed combustion boiler
(Maple)Explosion of a rich propane mixture
(Maple)Rich methane combustion
(MapleNatural gas heater
(MapleHydrogen production by partial oxidation
(MapleRich n-butane combustion
(MapleGas turbine combustion diluted with CO2
(MapleKerosene consumption in a gas turbine
(MapleDual fuel engine feed from LNG
(MapleFuel consumption and humidification in a fuel cell
(MapleFuel consumption in a gas turbine
(MapleCO2 emissions from a diesel engine
(MapleCO2 emissions from a diesel engine
(MapleMethanol injection in an air-filled vessel
(Maple)Burning naphthalene in a bomb calorimeter
(Maple)Burning propane with excess air
(MapleFuel consumption in a gas turbine
(MapleDry base analysis of exhaust gases
(MapleMethane combustion
(Maple)Jet A-1 heating value
(Maple)Burning decane with 3% excess air

(Maple)Shuttle fuels burning at lift off
(Maple)Dry-base data in a kerosene combustor
(Maple)Very rich H2/O2 combustion
(Maple)Rich combustion of n-octane/air
(Maple)Fuel efficiency and emission data of a diesel car

(Maple)Gasoline with ethanol
(Maple)Boiler with biogas
(Maple)Lean mix and rich mix of methane with air
(Maple)Gas turbine with a hydrogen/steam fuel mix
(Maple)Combustion in separate reactors with O2 carrier
(Maple)Combustion of a rich mixture at constant volume

Combustion processes: modelling

(Maple)Burning carbon monoxide
(Maple)Coal reforming
(Maple)Burning carbon monoxide at constant volume
(Maple)Air decomposition at high temperature
(Maple)Thermal run away in a vessel
(Maple)Laminar deflagration within a soap bubble
(Maple)Burning methane with pure oxygen
(Maple)Burning n-octane in a turbine
(Maple)Burning propane with pure oxygen
(Maple)Kinetics of nitrogen oxides
(Maple)Spherical deflagration within a vessel
(Maple)Thermal run away in ammonium nitrate
(Maple)Benzene drop burning
(Maple)Deflagration within a open/open tube
(Maple)Deflagration within a close/close tube

(Maple)Diffusion in a bunsen rim
(Maple)Burnin hydrogen with air
(Maple)Decomposition of nitrogen oxides
(Maple)Heat recovery for methane rectification
(Maple)Diffusion in a bunsen rim
(Maple)Variation of alkane data with carbon number
(Maple)Horizontal conical burner
(Maple)Equilibrium nitrogen monoxide
(Maple)Controlled exhaust oxygen fraction
(Maple)Methanol diffusion
(Maple)Ethanol diffusion
(Maple)Droplet combustion of n-octane in air
(Maple)Droplet combustion of n-heptane in air
(Maple)Equilibrium composition
(Maple)Symmetric deflagration within an open tube
(Maple)Combustion modelling of a gasoline engine (pdf)

Thermodynamics of power generation

(Maple)Ideal gas cycle efficiencies
(Maple)Energy and exergy analysis of a steam cycle (pdf)
(Maple)Regenerative Rankine cycle
(Maple)Butane vapour engine
(Maple)Gas cycle with two turbines
(Maple)Brayton-Rankine power plant
(Maple)Cogenerating plant
(Maple)Steam power plant modifications
(Maple)Cogeneration steam plant with regeneration
(Maple)Combined heat and power plant
(Maple)Steam cycle with reheating and regeneration
(Maple)Combined heat and power plant
(Maple)Combined cycle plant with regenerators
(Maple)Diesel cycle
(Maple)Gas turbine power plant
(Maple)Gas turbine power plant
(Maple)Gas turbine with underground air storage
(Maple)Boiler substitution by fluidized coal
(Maple)Nuclear power plant
(Maple)Bench thrust of a jet engine
(Maple)Gas turbine
(Maple)Gas turbine
(Maple)Gas turbine electricity generation plant

(Maple)Hot gas generator
(Maple)Tanker power plant
(Maple)Cogeneration plant

(Maple)Steam power plant retrofitting
(Maple)Offshore natural gas power plant

(Maple)Gas turbine
(Maple)Natural gas pipeline power

(Maple)Steam plant with open reheater
(Maple)Gas turbine for electricity generation

(Maple)Solar powered butane vapour plant
(Maple)Gas turbine for wajer-jet propulsion
(Maple)Gas turbine data
(Maple)Gas turbine with aspirated exhaust
(Maple)Combined cycle power plant
(Maple)Several ideal gas cycles (pdf)
(Maple)Combined cycle power plant (pdf)
(Maple)Gas turbine with exhaust heat recovery
(Maple)Steam turbine for a LNG-carrier
(Maple)Steam turbine driving a gas turbine
(Maple)Supercritical CO2 heat-engine
(Maple)Gas consumption in a combined-cycle power plant
(Maple)Rankine cycle for a geothermal source
(Maple)Otto cycle
(Maple)Combined cycle power plant
(Maple)Turbo-propeller cycle
(Maple)Water addition in a gas turbine
(Maple)Power generation in a LNG regasifying plant
(Maple)Organic Rankine cycle using pentane
(Maple)Transcritical CO2 cycle
(Maple)Demo turbojet
(Maple)Combined Brayton-Rankine cycle
(Maple)Cogeneration with micro gas turbine
(Maple)Brayton cycle for a space power plan
(Maple)Compressed air energy storage
(Maple)Power demanded by an airboat propeller
(Maple)Exergy destruction in a combined cycle's boiler
(Maple)Substitution of turbocombresor turbine by steam turbine
(Maple)Nuclear power plant for spacecraft
(Maple)Micro-turbojet test
(Maple)Gas turbine with external combustion
(Maple)Power from residual heat with a pentane cycle

Thermodynamics of refrigeration and heat pumps

(Maple)Basic refrugeration cycle with R134a
(Maple)Sinple and cascade refrigerators
(Maple)Sinple and cascade refrigerators
(Maple)Basics of refrigeration
(Maple)Stream cooling
(Maple)Producing high-speed cold air
(Maple)Heat pump for an ice rink
(Maple)Air dehumidification
(Maple)Producing liquid nitrogen (pdf)
(Maple)Producing liquid ethylene
(Maple)Producing dry ice
(Maple)Refrigerator with liquid undercooling
(Maple)Sun-powered heat pump
(Maple)Swimming pool conditioning
(Maple)Air conditioning
(Maple)Air conditioning
(Maple)Ammonia boil-off recirculation
(Maple)Cellar dehumidification
(Maple)Test chamber cooling
(MapleWater stream cooling

(Maple)Refrigeration with liquid undercooling
(Maple)Air stream cooling
(Maple)Large building climatisation

(Maple)Swimming pool conditioning
(Maple)Fish quick freezing
(Maple)Geothermal heat pump
(Maple)Heat pump for drying malt

(Maple)Refrigeration with ice storage
(Maple)Basic refrigeration cycle

(Maple)Basic refrigeration cycle (pdf)
(Maple)Cooling a water stream (pdf)
(Maple)No frost heat pump
(Maple)Air dehumidifying in an indoor swimming pool
(Maple)Dehumidifying an air stream
(Maple)Ammonia cooled freezing tunnel
(Maple)Binary refrigeration cycle
(Maple)Transcritical CO2 heat-pump
(Maple)Deshumification by refrigeration
(Maple)Air conditioning refrigeration
(Maple)Cascade cycle refrigeration
(Maple)Refrigerator with two vaporisers
(Maple)Cooling an air stream
(Maple)Cooling an air stream
(Maple)Cooling an air stream with a NH3 refrigerator
(Maple)Cooling an air stream with an R134a refrigerator
(Maple)Aircraft air conditioning at cruise
(Maple)Water condensation in a R134a heat pump
(Maple)Refrigerator using propane
(Maple)Car air conditioning
(Maple)Ideal Stirling cycle
(Maple)Backpack refrigerator
(Maple)Car air conditioning
(Maple)Cooling in a wing tip by expansion of ram air
(Maple)Hydrogen liquefaction
(Maple)Car air conditioning
(Maple)Heat pump using n-butane
(Maple)Aircraft air conditioning on ground
(Maple)Refrigeration cycle with diabatic capillary tube
(Maple)Refrigerator powered by a thermal engine
(Maple)Refrigerator to cool a gas turbine intake

Energy management: resources and contamination


Design of thermal systems


Thermal metrology