Specific Heat Capacity of Wood

Specific heat capacity is defined as the amount of heat that a kilogram of a given substance is required to absorb in order to increase its temperature by one degree. The temperature of a given substance can change either at constant pressure or at constant volume, so we differentiate between specific heat capacity at constant pressure (cp) and specific heat capacity at constant volume (cv). When doing research into the heat properties of wood, the quantity that most frequently remains constant is pressure, thus restricting our study on specific heat capacity to cp. This paper provides an overview of the research that has so far been carried out into the specific heat capacity of wood depending on the temperature and moisture content. An analytical and graphical comparison has been performed of the results published in the Wood Industry Manual (1967) (DIP), Wood Handbook (1999) (WH) and work published by Deliiski (2012) (DEL).


INTRODUCTION 1. UVOD
The thermal properties of wood are essential physical properties, especially in the processes of drying, producing heat energy by combustion and other processes, which include the transfer of heat through wood.The thermal properties of wood are as follows: specifi c heat capacity (c), coeffi cient of thermal conductivity (k) and thermal diffusivity (α).These three properties of wood are interconnected by the expression: (1) where: α -thermal diffusivity, m 2 •s -1 , k -coeffi cient of thermal conductivity, W/m•K, c -specifi c heat capacity, J/kg•°C, ρ -density, kg•m -3 .
Wood, being a porous biomaterial, contains small holes that greatly infl uence the mechanism of heat transfer, and therefore also the specifi c heat capacity.Generally speaking, wood is a porous system composed of gas (air), liquid (water) and solid matter (wood).Water can be bound or free, and appears in a solid or liquid state (Chudinov, 1968;Twardowski et al., 2006) stance in a temperature range of 0 °C to 112 °C.These results led to the conclusion that specifi c heat capacity does not depend on wood species or bulk density.The measurement results showed a linear dependence of specifi c heat capacity on the temperature ranging from 0 °C to 100 °C, as demonstrated by equation (4).On the basis of the data obtained by measurement, the value of constant A and B in equation ( 4) was determined.In the temperature range of 100 °C to 112 °C no connection between c p0 and temperature was established; on the basis of the data obtained by measurement, the average specifi c heat capacity for the given temperature interval was determined by means of equation (5) and it is 1.3688 kJ/kg•°C. where: A -constant that represents specifi c heat capacity at 0 °C, B -constant that represents the slope of a line, t -temperature. ( where: -mean specifi c heat capacity, J/kg•°C, c p -specifi c heat capacity, J /kg•°C, t 0 -initial temperature, °C, t 1 -fi nal temperature, °C.Dunlop (1912), Volbehr (1896) and Koch (1969) measured the c p0 for several types of wood in a temperature range of 0 °C to 100 °C, while Kanter (1957) measured the specifi c heat capacity in a temperature range of -40 °C to 100 °C.The data obtained by the aforesaid authors showed a linear dependence of c p0 on temperature.On the basis of the data obtained by measurement, coeffi cients A and B (Table 1) in equation (4) were determined.Coeffi cient A represents c p0 at the temperature of 0 °C, and coeffi cient B determines the slope of the line.These results led to the conclusion that c p0 does not depend on the wood species, density or specifi c weight.
Table 1 clearly shows that the data published by certain researchers (Dunlop, 1912;Volbehr, 1896;Koch, 1969) are only slightly different, while the data of the research done by Kanter (1957) coincides closely with the other authors in constant B, whereas the specifi c heat capacity at 0 °C is signifi cantly different from the values obtained by the other authors.However, apart from Kanter (1957), none of the other au-wood corresponds to its maximum hygroscopy, i.e. the moisture that the wood absorbs when the relative humidity of air equals 100 %.Maximum hygroscopy is called the fi ber saturation point (u fsp ) .The fi ber saturation point depends on the type and density of wood.
In view of the structure of wood, it is considered that the specifi c heat capacity of wood (c pw ) is a sum of the specifi c heat capacity of a dry wood substance (c p0 ), the specifi c heat capacity of free water (c pfw ) and the specifi c heat capacity of bound water (c pbw ) (Deliiski, 2012).
where: c pw -specifi c heat capacity of wood, J/kg•°C, c p0 -specifi c heat capacity of wood of dry wood substance, J/kg•°C, c pfw -specifi c heat capacity of free water, J/kg•°C, c pbw -specifi c heat capacity of bound water, J/kg•°C.
If the volume of water is below the fi ber saturation point, all of the water is bound, thus reducing the aforementioned expression to: The specifi c heat capacity of free and bound water depends on the state of matter.Free and bound water change their state of matter at different temperatures.Free water in wood changes its state of matter in a temperature range of -2 °C to -0.1 °C, depending on the concentration of dissolved sugar in water (Kubler et al., 1964;Chudinov, 1968), whereas bound water undergoes only a partial phase change in a wide temperature range at temperatures lower than -2 °C.

SPECIFIC HEAT CAPACITY OF DRY WOOD SUBSTANCE 2. SPECIFIČNI TOPLINSKI KAPACITET SUHE DRVNE TVARI
Over the course of the twentieth century, a lot of researchers dealt with the issue of the specifi c heat capacity of dry wood substance (c p0 ).The main reference point in this area is Dunlop's paper from 1912.In this paper, the c p0 is determined by means of a modifi ed Bunsen ice calorimeter.For the purposes of the experiment, the samples were cylindrical in shape, between 3 cm and 9 cm in length, 1.7 cm in base diameter.Out of a total of 110 samples, using 20 different wood species, varying from 0.23 and 1.10 in specifi c weight, Dunlop determined the specifi c heat capacity of dry wood sub-Table 1 Comparison of constants A and B in equation ( 4), average specifi c heat capacity of dry wood substance in a temperature range of 0 °C to 100 °C and average specifi c heat capacity of dry wood substance in a temperature range of -40 °C to 100 °C according to the research by Dunlop (1912), Volbehr (1896), Koch (1969) and Kanter (1957) Tablica 1. Usporedba konstanti A i B u jednadžbi (4), srednji specifi čni toplinski kapacitet suhe drvne tvari u temperaturnom rasponu od 0 do 100 °C i srednji specifi čni toplinski kapacitet suhe drvne tvari u temperaturnom rasponu od -40 do 100 °C prema istraživanjima Dunlopa (1912.),Volbehra (1896.),Kocha (1969.)(6) where: -mean specifi c heat capacity of wood fi ber, kJ/kg•°C, u -moisture content, %, t -temperature, °C Expression (6) served as a means to determine the with the wood moisture content between 0 % and 25 % in a temperature range of 0 °C to 100 °C.The obtained values can be seen in Figure (1).
Volbehr's research is tangible proof of the infl uence of the wood moisture content on the specifi c heat capacity of wood fi bers.Kanter (1957) determines the specifi c heat capacity of pine, oak and birch in a temperature range of -40 °C to 100 °C, with the moisture content varying between 0 % and 130 % (Figure 2).This data leads to the conclusion that the specifi c heat capacity of wood depends on the temperature and moisture content, while the variations between different wood species were very small.
The dependence of c pw on temperature is linear in a range of moisture content from 5 % to 30 %, but for temperatures below 0 °C this dependence is broken into two lines with a different slope coeffi cient.This change in slope coeffi cients occurs at the temperature at which change in the phase of bound water ends.
For wood moisture content higher than 30 %, the dependence of c pw on temperature is also linear with a sudden rise at a temperature slightly lower than 0 °C.This sudden rise is due to a change in the phase of free thors provides such high values of the specifi c heat capacity at the temperature of 0 °C.
It should be noted that Wilkes and Wood (1949) determined the average specifi c heat capacity of 1.427 kJ/kg•°C of a fi berboard, the density of which was 0.232 g/cm 3 , in a temperature range of 27 °C to 100 °C.
For the same temperature interval, the result of 1.421 kJ/kg•°C is obtained by the Dunlop equation (1912), which differs slightly from Wilkes and Wood.Using the Kirsher method of measuring the specifi c heat capacity, Kühlman (1962) obtained values very similar to those obtained by Dunlop.Different sample preparations and use of different measuring devices provide an explanation for the subtle differences in the results.
Several authors (Brown et al., 1952;Emchenko, 1958;Tiemann, 1951)  Volbehr (1896) determines the average specifi c heat capacity of wood fi bers in a temperature range of 0 °C to 100 °C, with the wood moisture content (u) varying between 0 % and 30 %.In the said temperature range and moisture content, the higher than the of dry wood substance in the same temperature range.On the basis of the data obtained by measurement, he draws the conclusion that , from depending on a change in temperature, also depends on the volume of water.The mathematical dependence of on the temperature and volume of water is shown in expression (6).Kuhlman (1962) determines the specifi c heat capacity of spruce, oak and beech wood in a temperature range of -60 °C to 80 °C, with the moisture content below 30 %, by means of two different methods (the Esdorn -Kirsher method and the ice calorimeter method).Contrary to Kanter (1957), there were no signifi cant changes in the specifi c heat capacity due to a change in the phase of bound water.The obtained values are considerably lower than those obtained by Kanter, but they coincide closely with the values obtained by the other authors at temperatures higher than 0 °C.Table 2 shows the average deviations of the available results of the other authors from Kanter's results.
Most of the authors arrive at the conclusion that the specifi c heat capacity of wood depends on the temperature and moisture content, while variations between wood species are very small.The available literature provides only two papers that mention greater variations between wood species.Narayanamurti et al. (1958) measured the specifi c heat capacity of nine Indian wood species (probably at room temperature), and the results cover the interval of (1.29 to 1.73) kJ/kg•°C.Koch (1969)  of earlywood and latewood, as well as of hardwoods and softwoods.The results also suggest the possibility of variations between different types of wood.Theoretical research into the specifi c heat capacity of wood was also directed at establishing a model of heat diffusion in the wood.A model that provides a satisfactory description of the change in the specifi c heat capacity with the change in the temperature and moisture content is obtained by solving the Fourier-Kirchhoff equation (Deliiski, 2012).

RASPRAVA
Due to the difference in results obtained by many authors, a comparison was drawn between the theoretical research conducted by Deliiski (2012) (DEL) and the research mentioned in the Wood Handbook (1999) (WH) and the Wood Technology Handbook (1967) (DIP).The temperature interval selected for the comparison was between 10 °C and 100 °C, and it results from a cross section of temperature intervals found in the literature.By means of equations from the studied literature, the specifi c heat capacity of wood was determined for a moisture content below the fi ber saturation point (Figure 3) and for a moisture content above the fi ber saturation point (Figure 4).It was assumed that the fi ber saturation point corresponds to 25 % moisture content.Figures 3 and 4 clear-ly show that the research confi rmed a linear dependence of the specifi c heat capacity of wood on temperature in the given temperature interval.The linearity is only disturbed in the Deliiski equation, but the term disturbing the linearity is very small; it equals , order of magnitude of which is 10 -4 .It should be noted that the results of the research mentioned in DIP cite the same equation of dependence of specifi c heat capacity on temperature, independent of the fi ber saturation point.The equation of dependence of specifi c heat capacity on temperature in the research mentioned in the Wood Handbook is true in a temperature range of 7 °C to 147 °C, but the equation contains a linear dependence of c p0 on temperature, which, according to Dunlop's research, is linear in a temperature range of 0 °C to 100 °C.By means of equation ( 5), the expression for the specifi c heat capacity was determined in a temperature range of 10 °C to 100 °C.The obtained average values are represented by equations ( 7), ( 8) and ( 9) for a moisture content below the fi ber saturation point, and by equations ( 10), ( 11) and ( 12) for a moisture content above the fi ber saturation point.Using the above equations, the average values of specifi c heat capacity were obtained for a moisture content between 0 % and 20 % (Figure 5) and for a moisture content between 80 % and 100 % (Figure 6).It is assumed that the fi ber saturation point corresponds to 25 % wood moisture content.

Table 2
published the results on the specifi c heat capacity The average deviations of the results of the other authors from Kanter's results for temperatures lower and higher than 0 °C and moisture content below and above 30 % (The USDA forest service general technical report FPL9, 1977) Tablica 2. Srednja odstupanja rezultata ostalih autora od Kanterovih rezultata za temperature manje i veće od 0 °C te za sadržaj vode manji i veći od 30 % (USDA forest service general technical reportFPL9, 1977.) (Kanter, 1957.ence of specifi c heat capacity of wood on temperature(Kanter, 1957)and wood moisture content between 0 % and 130 % Slika 2. Ovisnost specifi čnoga toplinskog kapaciteta drva o temperaturi(Kanter, 1957.)za sadržaj vode od 0 do 130 %