Heat and Heat and temperaturetemperature

A tube passes steam from a container of boiling water into a saturated aqueous salt solution. Can it be heated by the

steam to a temperature greater than 100 °C? Investigate the phenomenon

ResearchResearch

• Divided in phases:Divided in phases:• Basic explanationBasic explanation• Achieving the effect:Achieving the effect:

First apparatusFirst apparatusSecond apparatusSecond apparatus

• MeasurementMeasurement• Theoretical approachTheoretical approach• Comparison Comparison

Basic explanationBasic explanation

• Changes when salt is dissolved in Changes when salt is dissolved in water:water:

• Density (increases)Density (increases)• Vapour pressure (falls)Vapour pressure (falls)• Boiling point (increases)Boiling point (increases)

Bubbles of water vapour at 100°C are able Bubbles of water vapour at 100°C are able to condense in water – salt solution up to its to condense in water – salt solution up to its boiling pointboiling point

solution heated to its boiling point by latent solution heated to its boiling point by latent heat of condensationheat of condensation

• Boiling point increase:Boiling point increase:

• For water and NaCl:For water and NaCl:

• For larger effect – different saltsFor larger effect – different saltsKK22COCO33 – 15.8 K – 15.8 K

Basic explanation Basic explanation cont.cont.

sb m

nKT

ε – number of particles the salt dissociates toKe [K mol-1 kg] – ebulioscopic constant (for water 0,52)n – molarms – solvent mass

K 5.3T

Achieving the effect Achieving the effect (apparatus 1)(apparatus 1)

• An U - An U - tubetube• Effect not achievedEffect not achieved• Contact betwen Contact betwen

bubble of vapour and bubble of vapour and solution too shortsolution too short

• Container with Container with solution too narrowsolution too narrow

• Turbulences appearTurbulences appear

Achieving the effect Achieving the effect (apparatus 2)(apparatus 2)

• Changes inChanges in second second apparatus:apparatus:• longer contact longer contact

betwebetweeen n vapour vapour bubbles bubbles and and solutionsolution

• Wider Wider tubetube

MeasuringMeasuring

• Measured: vapour and solution Measured: vapour and solution temperatures in timetemperatures in time

• Parameters:Parameters:• Vapour mass flow rate (varied by Vapour mass flow rate (varied by

heater power change)heater power change)• Solution level in tube (held constant)Solution level in tube (held constant)

• Most measurements with NaClMost measurements with NaCl• KK22COCO33 used for demonstrating higher used for demonstrating higher

temperatures above 100°Ctemperatures above 100°C

ApparatusApparatus

• Vaporisation chamberVaporisation chamberErlenmayer tikvicaErlenmayer tikvicaHeaterHeater

• Set of pipes and gaugesSet of pipes and gauges• Testing tube to contain solutionTesting tube to contain solution• Thermometer systemThermometer system• Electronic supportElectronic support

HardwareHardwareSoftwareSoftware

Apparatus Apparatus cont.cont.

Thermometer 2

Thermometer 1

Thermometer 3

Gauge Heater

Deionized water

Solu

tion

Apparatus Apparatus cont.cont.

Apparatus - electronicsApparatus - electronics

Thermometer 1

Thermometer 2

Thermometer 3

Signal conditioning

Multiplexer

Motherboard

ADC Computer

Apparatus – electronics Apparatus – electronics cont.cont.S

ign

al

con

dit

ion

ing

Multiplexer

Motherboard

Theoretical approachTheoretical approach

• Goal: modeling the time evolution of Goal: modeling the time evolution of solution temperaturesolution temperature

• Heat transfer – condensation/latent heatHeat transfer – condensation/latent heat– – losseslosses

• Two distionct regions:Two distionct regions:• Temperature far from solution boiling Temperature far from solution boiling

point (steam bubbles absorbed)point (steam bubbles absorbed)• Temperature close to boiling point Temperature close to boiling point

(bubbles mostly pass through)(bubbles mostly pass through)

Theoretical approach Theoretical approach cont.cont.

• Simplified heat transfer equation in the Simplified heat transfer equation in the solution:solution:

• Mass of condensed water – time dependent:Mass of condensed water – time dependent:

LdmdQdTcmM ds

M – initial solution massm – mass of condensed

watercs – solution heat capacityT – temperatureQd – heat lossL – water latent heat of

evaporation

dtmdm pΓ – number of bubbles in

unit time (flow rate!)Δmp – mass of condensed

steam per bubble

Theoretical approach Theoretical approach cont.cont.

• In Region 1 whole bubble absorbed:In Region 1 whole bubble absorbed:

• In Region 2 bubble partially absorbed – In Region 2 bubble partially absorbed – complicated theorycomplicated theory

• Asymptotic behaviour determinable – Asymptotic behaviour determinable – bubble equation of motionbubble equation of motion

dtmLdQdTMctM

mpds

p

1

Theoretical approach Theoretical approach cont.cont.

• If losses are known, analytic solution in If losses are known, analytic solution in Region 1 possibleRegion 1 possible

• Losses:Losses:• Conduction through tube walls & airConduction through tube walls & air• Evaporation lossEvaporation loss

• Net losses – in first order linear in Net losses – in first order linear in temperature:temperature:

id TTdt

dQ

Qd – loss

Λ – constantT – solution temperatureTi – surroundings

temperature

Theoretical approach Theoretical approach cont.cont.

• Evidence – experimental:Evidence – experimental:

time [s]

0 1000 2000 3000 4000 5000

tem

pera

ture

/100

[K]

3,1

3,2

3,3

3,4

3,5

3,6

3,7

exponential fitmeasurement

ComparisonComparison

-1K 130

time [s]

0 100 200 300 400 500 600

tem

pera

ture

/100

[K]

2,8

3,0

3,2

3,4

3,6

3,8

4,0

4,2

theorysolutionsteam

Comparison Comparison cont.cont.

time [s]

0 500 1000 1500 2000 2500 3000

tem

pera

ture

/100

[K]

2,8

3,0

3,2

3,4

3,6

3,8

theory80,5 W115,5 W150,4 W 224,0 W

Comparison Comparison cont.cont.

Additions Što ne znam na engleskom? Ako netko

zna nek napiše Otapalo solvent Množina Disocirati Tikvica (elermayerova) Ventili ventils??? epruveta