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Explanation of the Thermodynamic Anomalies of Water (T1-T11)

V The heat of fusion of water with temperature exhibits a maximum at -17 °C
V Water has over twice the specific heat capacity of ice or steam
V The specific heat capacity (CP and CV) is unusually high
V The specific heat capacity CP has a minimum at 36°
V The specific heat capacity (CP) has a maximum at about -45 °C
V The specific heat capacity (CP) has a minimum with respect to pressure
V The heat capacity (CV) has a maximum
V High heat of vaporization
V High heat of sublimation
V High entropy of vaporization
V The thermal conductivity of water is high and rises to a maximum at about 130 °C

T1   The heat of fusion of water with temperature exhibits a maximum at -17 °C.

Enthalpy of fusion of hexagonal ice at 101325 Pa; [15]


This strange behavior [15 ] (see right) 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 the 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 CSreversible arrowES 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.

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T2    High specific heat capacity

Water has the highest specific heat a of all liquids except ammonia. The values for CV and CP are 4.1375 J g-1 K-1 and 4.1819 J g-1 K-1at 25 °C respectively (compare CP pentane 1.66 J g-1 K-1). 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. Thus, the water in our oceans stores vast amounts of energy, so moderating Earth's climate. [ link  Anomalies page: Back to Top to top of page]

T3    Water has about twice the specific heat capacity of ice or steam

At its melting point, the CP a of ice-Ih and water are 37.77 J mol-1 K-1 and 76.01 J mol-1 K-1 respectively. At its boiling point the CP of steam and water are 37.47 J mol-1 K-1 and 75.95 J mol-1 K-1 respectively (compare with benzene where CP liquid = 1.03 ˣ CP solid). 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. [link  Anomalies page: Back to Top to top of page]

T4    The specific heat capacity (CP) has a minimum at 36 °C.

It is usual for the isobaric specific heats (CP) a of liquids to increase with increased temperature at all temperatures.


Variation of Cp and Cv with temperature at 100 kPa

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 at 100 kPa (D2O ~120 °C) with a particularly steep negative slope below 0 °C [15, 67] (see right). It is interesting that this minimum is close to the body temperature of warm-blooded animals. The water cluster equilibrium shifts towards less structure (for example, CS) and higher enthalpy as the temperature is raised.

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.



heat capacity at 400 MPa, from [2929]


Modeling studies using TIP4P/2005 has shown that this minimum goes to higher temperatures at higher pressure [2668 ].


As expected, the large specific heat changes with temperature at low temperatures are reduced at higher pressures and this specific heat-pressure minimum shifts to lower temperatures and disappears at high pressures (> 100 MPa, see above). 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].


A further anomaly is found at higher pressure (see left) where two maxima may be found at 400 MPa [2929 ]. The anomaly at this pressure is due to the interpenetration of water clustering (see elsewhere). [link  Anomalies page: Back to Top to top of page]


T5    The specific heat capacity (CP) has a maximum at about -45 °C.

Heat capacity changes for supercooled (amorphous) liquid water and hexagonal ice

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 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 ].


Modeling studies using TIP4P/2005 has shown that this maximum goes to lower temperatures at higher pressure and increases to higher temperatures under negative pressure [2668 ].

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T6    The specific heat capacity (CP) has a minimum with respect to pressure.

Please note that this anomaly is in doubt until the data is confirmed.

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. [link  Anomalies page: Back to Top to top of page]

T7    The heat capacity (CV) has a maximum.

The CV (the heat capacity at constant volume, CV = (δU/δT)V) of liquid water gives a maximum in the supercooled region (shown in the calculated values graphed above). The increase in CV 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 more deeply supercooled region is reported as due to the decrease in van der Waals non-bonded dispersion interactions, due to water's low-density [682 ] and is clear in the calculation (using CP=CV+temperature*molar volume*expansivity^2/compressibility where T = temperature (K), V = molar volume (m3 mol-1), α = thermal expansivity (K-1) and κ T= isothermal compressibility (Pa-1) as due to the great increase in the values of the thermal expansivity at low temperatures, see table [2218 ]). [ link  Anomalies page: Back to Top to top of page]

T8    High heat of vaporization (40.7 kJ ˣ mol-1, compare H2S 18.7 kJ ˣ mol-1)

Comparison of the molar enthalpy of evaporation at boiling points  with related structures

Water has the highest heat of vaporization per gram of any molecular liquid (2257 J g-1 at boiling point) and hence a very low volatility but high cohesive energy density (~5 ˣ CH4, ~4 ˣ H2S). 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 ˣ mol-1, at 0 °C).


Enthalpies of evaporation and fusion of molecules isoelectronic to water Ne, Fusion 0.34 kJ/mol; evaporation 1.74 kJ/mol HF, 4.56 kJ/mol HF, 25.20 kJ/mol NH3, 7.70 kJ/mol NH3, 17.52 kJ/mol CH4, 8.16 kJ/mol H2O, 6.01 kJ/mol CH4, 0.096 kJ/mol H2O, 40.66 kJ/mol

Variation of the enthalpy of evaporation with temperature


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, the 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.


The high heat of vaporization allows fine water mists to be used in fighting fires by cooling flames [2456].


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T9    High heat of sublimation (51.059 kJ ˣ mol-1 at 0 °C).

The high heats of fusion and vaporization combine to give rise to an anomalously high heat of sublimation. [link  Anomalies page: Back to Top to top of page]

T10    High entropy of vaporization (109 J-1 K mol-1, compare Trouton's constant ~87 J K-1 mol-1).

Water also has an 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 the temperature of supercooled water to above 400K (that is, ΔSvap is proportional to 1/T). [link  Anomalies page: Back to Top to top of page]

T11    The thermal conductivity of water is high and rises to a maximum at about 130 °C.

The thermal conductivity of water, the supercooled data is from [1983]

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].


Additionally, If carefully drawn using the original data (rather than a smoothed curve), there appears to be a kink at about 64 °C [2755, 2756].


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 ESreversible arrowCS 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.


If our cells produce excess energy, that heat energy is transported away more efficiently at higher temperatures, so reducing its heating effect. At lower temperatures, with lower thermal conductivity, the heat is less well transported away so allowing greater heating effect. Thus our cells are more able to stabilize their temperature.


There is a minimum in the thermal conductivity-temperature behavior just below -37 °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]. Different modeling approaches give a thermal conductivity minimum at ~255 K [1352] or ~230 K [1983].


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]. [link  Anomalies page: Back to Top to top of page]


a The heat capacity (C) is the ratio of the heat added (Q) or subtracted to an object to the resulting temperature change (≡ Q/ΔT). The specific heat (capacity) is the heat capacity per unit mass of a material. CP and CV are the heat capacities at constant pressure (isobaric) and constant volume (isochoric) respectively.


As H = U + PV and δQ = dU + PdV, CP = (δH/δT)P and CV = (δU/δT)V , where U is the internal energy and H is the sysytem enthalpy.

The full expressions are


 CP = (δH/δT)P= T(δS/δT)P<(ΔS)2>TP /kB<(ΔH)2>TPN /kBT2 = (δU/δT)P + PVαV


 CV = (δU/δT)V= T(δS/δT)V = (δH/δT)V - PVαP = CP - TVαP2T


where kB, P, T, N, V, H, S, αV, αP and κT are the Boltzmann constant, pressure (Pa), temperature (K), number of molecules, specific volume (V=1/density; m3 mol-1), enthalpy, entropy, isobaric cubic expansion coefficient (αV=(δV/δT)P/V ; K-1), relative pressure coefficient (αP=(δP/δT)V/P ; K-1) and isothermal compressibility (κT=-(δV/δP)T/V ; Pa-1) respectively; the <> brackets indicate the fluctuations in the values about their mean values.


(also see [1481]) [Back]







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This page was established in 2006 and last updated by Martin Chaplin on 31 July, 2017

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