The heat of fusion of water with temperature
exhibits a maximum at -17°C Water has over twice the specific
heat capacity of ice or steam The specific heat capacity (CP and CV) is unusually
high The specific heat capacity CP has a minimum at 36° The specific
heat capacity (CP) has a maximum at about -45°C The specific
heat capacity (CP) has a minimum with respect to pressure The heat capacity (CV) has a maximum High heat
of vaporization High heat of sublimation High entropy
of vaporization The thermal conductivity of water is
high and rises to a maximum at about 130°C This strange behavior has been determined from the variation
in ice and water specific heat capacities (Cp). It is
due to changes in the structuring of supercooled water. As the temperature
is lowered from 0°C the hydrogen-bond strength of ice increases
due to the reduction in their vibrational energy and this gives
rise to an increasing difference (as temperature is lowered) between
the enthalpy of the water and ice. At low temperatures (below about
-17°C) the continued shift, with lowering temperature, in the
supercooled water CS
ES equilibrium towards the ES structure reduces the enthalpy of the liquid water relative to the
ice due to the consequent increase in hydrogen-bond strength and
this causes the drop in the heat of fusion with lowering temperature.
[
Anomalies page : Back to Top 
]
Water has the highest specific heat of all liquids except
ammonia. As water is heated, the increased movement of water
causes the hydrogen bonds to bend and break. As the energy
absorbed in these processes is not available to increase the
kinetic energy of the water, it takes considerable heat to
raise water's temperature. Also, as water is a light molecule
there are more molecules per gram, than most similar molecules,
to absorb this energy. Heat absorbed is given out on cooling,
so allowing water to act as a heat reservoir, buffering against
changes in temperature.
[ Anomalies page : Back to Top ]
At its melting point the CPs of ice-Ih and water are 38 J mol-1 K-1 and 76 J mol-1 K-1 respectively.
The CP's of the other ices may be up to about 40% higher
(ice-three) than that of ice-1h but are
all significantly lower than liquid water [606].
The specific heats of polar molecules do increase considerably on
melting but water shows a particularly large increase [1723]. As water
is heated, much of the energy is used to bend the hydrogen bonds;
a factor not available in the solid or gaseous phase. This extra
energy causes the specific heat to be greater in liquid water. The
presence of this large specific heat offers strong support for the
extensive nature of the hydrogen-bonded network of liquid water.
[ Anomalies page : Back to Top ]
It is usual for the specific heats of liquids to increase with increased temperature at all temperatures.
The CV values for supercooled water may be erroneous, being calculated from other data and showing an apparent discontinuity at about -20°C. An alternative extrapolation is available [1794].
The (isobaric; also called isopiestic) specific heat capacity (CP) has a shallow minimum at about 36°C (D2O ~120°C) with a particularly steep negative slope below 0°C [15, 67]. The water cluster equilibrium shifts towards less structure (for example, CS) and higher enthalpy as the temperature is raised. CP is the heat capacity at constant pressure defined by
CP = (δH/δT)P= T(δS/δT)P 
<(ΔS)2>TP <(ΔH)2>TPN
(that is, equals change in enthalpy with temperature, and
proportional to the square of the entropy (or enthalpy) fluctuations).a The extra positive ΔH
due to the shift in equilibrium (at low temperatures)
as the temperature is raised causes a higher CP than otherwise, particularly at supercooling temperatures
where a much larger shift occurs [1353]. Note that generally thermal fluctuations (<(ΔS)2>TP) increase with increasing temperature whereas the reverse is true of supercooled water. This addition to the
CP, as the temperature is lowered, is greater
than the 'natural' fall expected, so causing a minimum
to be created. Note that CV equals CP at the temperature of maximum density. Usually in liquids
CP is more than 20% greater than CV.
It is expected that the large specific heat changes
with temperature at low temperatures will be reduced at
higher pressures and this specific heat-pressure minimum will shift
to lower temperatures. The minimum in CP has been associated with a discontinuity in the Raman depolarization ratio (that is, perpendicular/parallel polarization) data of degassed ultrapure water and hence a weak liquid-liquid phase transition at 34.6°C (5.8 kPa) [1044].
[ Anomalies page : Back to Top ]
There are large specific heat changes
with temperature at low temperatures but deeply supercooled water has lower specific heat at very low temperatures. At sufficiently low temperature,
there must be a maximum in the specific heat (CP)-temperature
relationship, so long as no phase change occurs. This maximum is thought to occur where where the amounts of expanded (low density) and collapsed (higher density) structures are equal and thus the most energy is required for their interconversion (using the icosahedral clustering model, this would be where there is 80% ES, as ES necessarily has a collapsed exterior surface). The locus of the specific heat maximum with increasing pressure (called the 'Widom' line) requires the temperature is lowered [1373]. At ambient pressure, the maximum
is expected to lie just below the minimum temperature
accessible on supercooling (232 K, [215]), although a modeling approach using TIP5P gives ~250 K [1352].
The data opposite for supercooled water (upper red line) is taken from [906].
[ Anomalies page : Back to Top ]
There is a minimum in the heat capacity (CP)
of liquid water with respect to pressure; ~400 MPa at 290 K [606].
This may be explained as due to the break-up of the hydrogen
bonding as the pressure increases up to about 200 MPa followed by its partial
build-up, due to interpenetrating hydrogen bonded networks,
at the higher pressures above about 200MPa.
[ Anomalies page : Back to Top ]
The CV (the heat capacity
at constant volume, CV = (δU/δT)V) of liquid water is reported as showing an opposite anomaly, giving a maximum
in the supercooled region (this is not shown in the calculated
values graphed above). The increase in CP in
the supercooled region is because most of the anomalous enthalpy
change is associated with the anomalous volume change. The
decrease in CV in the supercooled region is reported
as due to the decrease in van der Waals non-bonded interactions,
due to water's low density [682].
[ Anomalies page : Back to Top ]
Water has the highest heat of vaporization per gram of any molecular liquid (2257 J g-1 at boiling point). There is still considerable hydrogen bonding (~75%) in water at 100°C. As effectively all these bonds need to be broken (very few indeed remaining in the gas phase), there is a great deal of energy required to convert the water to gas, where the water molecules are effectively separated. The increased hydrogen bonding at lower temperatures causes higher heats of vaporization (for example, 44.8 kJ mol-1, at 0°C).
The heat of vaporization reduces to zero at the critical point (see left, [906, 1458]).
The high heat of vaporization also causes water to have an
anomalously low ebullioscopic constant (that is, effect
of solute on boiling point elevation, 0.51 K kg/mol, compare CCl4 4.95 K kg/mol).Also related is the anomalously low
cryoscopic constant of water.
[ Anomalies page : Back to Top ]
The high heats of fusion and vaporization combine to give
rise to an anomalously high heat
of sublimation.
[ Anomalies page : Back to Top ]
Water also has anomalously high entropy of vaporization due to the hydrogen-bonded order lost on vaporization in addition to the order lost by virtue of being a liquid changing into a gas. As the heat of vaporization is also anomalously high, the ratio (ΔHvap/ΔSvap) is not anomalous.
Interestingly, the entropy of vaporization is inversely related
to the absolute temperature from supercooled water to above
400K (that is, ΔSvap 1/T).
[ Anomalies page : Back to Top ]
Thermal conductivity along the saturation line (liquid-vapor equilibrium line). Note that the pressure increases with the temperature, see phase diagram. The thermal conductivity becomes infinite at the critical point [IAPWS].
Apart from liquid metals, water has the highest thermal conductivity of any liquid. For most liquids the thermal conductivity (the rate at which energy is transferred down a temperature gradient) falls with increasing temperature but this occurs only above about 130°C in liquid water [188].
As the temperature of water is lowered, the rate at which
energy is transferred is reduced to an ever-increasing
extent. Instead of the energy being transferred between
molecules, it is stored in the hydrogen bonding fluctuations
within the increasingly large clusters that occur at lower
temperatures. When the thermal energy
is increased it shifts the ESCS equilibrium towards the CS structure, which possesses greater flexibility and has
a greater number of bent hydrogen bonds, rather than the
transference of kinetic energy. It is likely that there
will be a minimum in the thermal conductivity-temperature behavior at about -30±15°C as the amount of
fully expanded network increases and in line with that indicated by the
much higher value found for ice Ih. At lower temperatures, transformation into LDA results in a steeply climbing curve (1.4 W K-1 m-1 at 100 K) [1202]. A modeling approach using TIP5P gives the minimum at ~255 K [1352].
If the density is kept constant the thermal conductivity
is proportional to the square root of the absolute temperature,
between 100°C and 400°C [614].
[ Anomalies page : Back to Top ]
CP = (δH/δT)P= T(δS/δT)P = <(ΔS)2>TP /kB = <(ΔH)2>TPN /kBT2
where kB, P, T, N, V, H and S are the Boltzmann constant, pressure, temperature, number of molecules, volume, enthalpy and entropy respectively; the <> brackets indicate the fluctuations in the values about their mean values.
Phase anomalies (P1-P12) explanations
Density anomalies (D1-D20) explanations
Material anomalies (M1-M12) explanations
Physical anomalies (F1-F9) explanations
Home | Site Index | The anomalies of water | Water: Introduction | The icosahedral water clusters | LSBU | Top
This page was last updated by Martin Chaplin on 18 April, 2012
