Heat and temperature
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
Research
• Divided in phases:
• Basic explanation
• Achieving the effect:
First apparatus
Second apparatus
• Measurement
• Theoretical approach
• Comparison
Basic explanation
• Changes when salt is dissolved in
water:
• Density (increases)
• Vapour pressure (falls)
• Boiling point (increases)
 Bubbles of water vapour at 100°C are able
to condense in water – salt solution up to its
boiling point
 solution heated to its boiling point by latent
heat of condensation
Basic explanation
cont.
• Boiling point increase:
n
T  K b
ms
ε – number of particles the salt
dissociates to
Ke [K mol-1 kg] – ebulioscopic
constant (for water 0,52)
n – molar
ms – solvent mass
• For water and NaCl:
T  5.3 K
• For larger effect – different salts
K2CO3 – 15.8 K
Achieving the effect
(apparatus 1)
• An U - tube
• Effect not achieved
• Contact betwen
bubble of vapour and
solution too short
• Container with
solution too narrow
• Turbulences appear
Achieving the effect
• Changes in
second
apparatus:
• longer contact
between
vapour
bubbles and
solution
• Wider tube
(apparatus 2)
Measuring
• Measured: vapour and solution
temperatures in time
• Parameters:
• Vapour mass flow rate (varied by
heater power change)
• Solution level in tube (held constant)
• Most measurements with NaCl
• K2CO3 used for demonstrating higher
temperatures above 100°C
Apparatus
• Vaporisation chamber
Erlenmayer tikvica
Heater
• Set of pipes and gauges
• Testing tube to contain solution
• Thermometer system
• Electronic support
Hardware
Software
Apparatus
Thermometer 2
cont.
Thermometer 3
Solution
Gauge
Thermometer 1
Heater
Deionized water
Apparatus
cont.
Apparatus - electronics
Thermometer 1
Thermometer 2
Signal
conditioning
Multiplexer
Thermometer 3
Motherboard
ADC
Computer
Apparatus – electronics
Multiplexer
Motherboard
cont.
Theoretical approach
• Goal: modeling the time evolution of solution
temperature
• Heat transfer – condensation/latent heat
– losses
• Two distionct regions:
• Temperature far from solution boiling
point (steam bubbles absorbed)
• Temperature close to boiling point
(bubbles mostly pass through)
Theoretical approach
cont.
• Simplified heat transfer equation in the
solution:
M – initial solution mass
M  mcs dT  dQd  Ldm
m – mass of condensed water
cs – solution heat capacity
T – temperature
Qd – heat loss
L – water latent heat of
evaporation
• Mass of condensed water – time dependent:
dm  mp dt
Γ – number of bubbles in unit
time (flow rate!)
Δmp – mass of condensed
steam per bubble
Theoretical approach
cont.
• In Region 1 whole bubble absorbed:
 m p

 
t  1 Mcs dT  dQd  Lm p dt
 M

• In Region 2 bubble partially absorbed –
complicated theory
• Asymptotic behaviour determinable – bubble
equation of motion
Theoretical approach
cont.
• If losses are known, analytic solution in
Region 1 possible
• Losses:
• Conduction through tube walls & air
• Evaporation loss
• Net losses – in first order linear in
temperature:
dQd
  T  Ti 
dt
Qd – loss
Λ – constant
T – solution temperature
Ti – surroundings temperature
Theoretical approach
• Evidence – experimental:
3,7
temperature/100 [K]
3,6
3,5
3,4
3,3
3,2
exponential fit
measurement
3,1
0
1000
2000
time [s]
3000
4000
5000
cont.
Comparison
4,2
temperature/100 [K]
4,0
3,8
3,6
3,4
3,2
  130 K
theory
solution
steam
3,0
2,8
0
100
200
300
time [s]
400
500
600
-1
Comparison
cont.
3,8
temperature/100 [K]
3,6
3,4
3,2
theory
80,5 W
115,5 W
150,4 W
224,0 W
3,0
2,8
0
500
1000
1500
time [s]
2000
2500
3000
Comparison
cont.
Additions
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
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Što ne znam na engleskom? Ako netko zna
nek napiše
Otapalo solvent
Množina
Disocirati
Tikvica (elermayerova)
Ventili ventils???
epruveta