Copper specific heat

A special attention is to be devoted to copper, which is very often used in a cryogenic apparatus. The low-temperature specific heat of copper is usually considered as given by c = 10-5 T [J/g K], However, an excess of specific heat has been measured, as reported in the literature [59-69], For 0.03 K < T< 2K, this increase is due to hydrogen or oxygen impurities, magnetic impurities (usually Fe and Mn) and lattice defects [59-66], The increase of copper specific heat observed in the millikelvin temperature range is usually attributed to a Schottky contribution due to the nuclear quadrupole moment of copper [67,68],... 

A llO.-g sample of copper (specific heat capacity = 0.20 J °C-1 g-1) is heated to 82.4°C and then placed in a container of water at 22.3°C. The final temperature of the water and copper is 24.9°C. What is the mass of the water in the container, assuming that all the heat lost by the copper is gained by the water ... 

Amongst heat stabilisers are copper salts, phosphoric acid esters,phenyl-3-naphthylamine, mercaptobenzothiazole and mercaptobenzimidazole. Of these, copper salts in conjunction with halides have been found particularly effective, and some automotive specifications require the use of copper for heat stabilisation. Light stabilisers include carbon black and various phenolic materials. 

Copper is used in building the integrated circuits, chips, and printed circuit boards for computers. When 228 J of heat are absorbed by 125 g of copper at 22.38°C, the temperature increases to 27.12°C. What is the specific heat of copper ... 

The method just described leads to the mean specific heats over a fairly large range. Nernst, Koref, and Lindemann (1910) have recently described a method of measuring the true specific heat at a given low temperature. The substance is contained in a block of copper cooled to the requisite temperature in liquid carbon dioxide, liquid air, etc., and energy is supplied by a heating spiral of platinum wire carrying an electric current, the measurement of the resistance of which serves at the same time to determine the temperature. 

Page 14, line 2 The method of Nernst, Koref, and Lindemann, by the use of the copper-calorimeter, determines the mean specific heat over a range of temperature. The mode of procedure is the same as in ordinary calorimetry, except that a hollow block of copper, the temperature of which is determined by means of inserted thermoelements, is used instead of a calorimetric liquid, and the method therefore made applicable to very low temperatures. 

E3.7 A block of copper weighing 50 g is placed in 100 g of HiO for a short time. The copper is then removed from the liquid, with no adhering drops of water, and separated from it adiabatically. Temperature equilibrium is then established in both the copper and water. The entire process is carried out adiabatically at constant pressure. The initial temperature of the copper was 373 K and that of the water was 298 K. The final temperature of the copper block was 323 K. Consider the water and the block of copper as an isolated system and assume that the only transfer of heat was between the copper and the water. The specific heat of copper at constant pressure is 0.389 JK. g l and that of water is 4.18 J-K 1-g 1. Calculate the entropy change in the isolated system. 

Even when complete miscibility is possible in the solid state, ordered structures will be favored at suitable compositions if the atoms have different sizes. For example copper atoms are smaller than gold atoms (radii 127.8 and 144.2 pm) copper and gold form mixed crystals of any composition, but ordered alloys are formed with the compositions AuCu and AuCu3 (Fig. 15.1). The degree of order is temperature dependent with increasing temperatures the order decreases continuously. Therefore, there is no phase transition with a well-defined transition temperature. This can be seen in the temperature dependence of the specific heat (Fig. 15.2). Because of the form of the curve, this kind of order-disorder transformation is also called a A type transformation it is observed in many solid-state transformations. 

Fig. 3.3. Specific heat c of copper divided by the temperature T as a function of T2 [8].

The magnetic specific heats of some alloys containing paramagnetic atoms together with copper for comparison are shown in Fig. 3.8. Note that below 0.1 K, magnetic materials as manganin have a specific heat 103 higher than copper. 

The low-temperature thermal conductivity of different materials may differ by many orders of magnitude (see Fig. 3.16). Moreover, the thermal conductivity of a single material, as we have seen, may heavily change because of impurities or defects (see Section 11.4). In cryogenic applications, the choice of a material obviously depends not only on its thermal conductivity but also on other characteristics of the material, such as the specific heat, the thermal contraction and the electrical and mechanical properties [1], For a good thermal conductivity, Cu, Ag and A1 (above IK) are the best metals. Anyway, they all are quite soft especially if annealed. In case of high-purity aluminium [2] and copper (see Section 11.4.3), the thermal conductivities are k 10 T [W/cm K] and k T [W/cm K], respectively. 

Dowden and Reynolds (49,50) in further experimental work on the hydrogenation of benzene and styrene with nickel-copper alloys as catalysts, found a similar dependence. The specific activities of the nickel-copper alloy catalysts decreased with increasing copper content to a negligible value at 60% copper and 30-40% copper for benzene and styrene, respectively. Low-temperature specific heat data indicated a sharp fall (1) in the energy density of electron levels N(E) at the Fermi surface, where the d-band of nickel becomes filled at 60 % copper, and (2) from nickel to the binary alloy 80 nickel -)- 20 iron. Further work by these authors (50) on styrene hydrogenation with nickel-iron alloy... 

A 200 g sample of an unknown high-boiling liquid is put into the calorimeter calibrated in Problem 25, and its temperature is observed to be 24.2°C. Then 55.3 g of copper at 180.0°C are added to the liquid in the calorimeter to give a resultant temperature of 28.0°C. Calculate the specific heat of the liquid. Use the approximate specific heat of copper. 

Heat capacities, C, are also reported for pure substances, not just for the complicated assembly of substances that makes up a typical calorimeter. For instance, we can report the heat capacity of water or of copper. More heat is needed to raise the temperature of a large sample of a substance by a given amount than is required to raise the temperature of a small sample by the same amount, so heat capacity is an extensive property the larger the sample, the greater its heat capacity (Fig. 6.15). It is therefore common to report either the specific heat capacity (often called just specific heat ), Cs, which is the heat capacity divided by the mass of the sample (Cs = dm), or the molar heat capacity, Cm, the heat capacity divided by the number of moles in the sample (Cm = dn). Specific heat capacities and molar heat capacities are intensive properties. 

Self-Test 6.7A A piece of copper of mass 19.0 g was heated to 87.4°C and then placed in a calorimeter that contained 55.5 g of water at 18.3°C. The temperature of the water rose to 20.4°C. What is the specific heat capacity of copper ... 

A piece of copper of mass 20.0 g at 100.0°C is placed in an insulated vessel of negligible heat capacity but containing 50.7 g of water at 22.0°C. Calculate the final temperature of the water. Assume that all the energy lost by the copper is gained by the water. The specific heat capacity of copper is 0.38 J-(°C) 1-g 1. 

The specific heat at constant pressure, Cpf of the HIP-treated sample with nominal composition LaVg 25 0,7504 was measured over the temperature range 4-400 K by the heat pulse method in a calorimeter that incorporates a feedback system to regulate the temperature of concentric radiation shields surrounding the sample (9). The Cp values are accurate to within 1%, as determined by calibration runs using a polycrystalline copper sample and a sapphire single crystal sample. 

Exactly three grams of carbon were burned to CO2 in a copper calorimeter. The mass of the calorimeter is 1500 g and the mass of the water in the calorimeter is 2000 g. The initial temperature was 20.0°C and the temperature rose to 31.3°C. Calculate the heat of combustion of carbon in joules per gram. The specific heat of copper is 0.389 J/g K. 

We are now equipped with the necessary tools to solve problems involving specific heat and heat flow. Imagine a 10.0 g sample of copper that undergoes an increase in temperature from 25.0 to 100 °C when 289 J of heat is added. What is the specific heat of copper ... 

We are asked to calculate the specific heat of copper. We can easily do this using the definition of specific heat, ensuring that we use the proper SI units. 

In conclusion, field dependent single-crystal magnetization, specific-heat and neutron diffraction results are presented. They are compared with theoretical calculations based on the use of symmetry analysis and a phenomenological thermodynamic potential. For the description of the incommensurate magnetic structure of copper metaborate we introduced the modified Lifshits invariant for the case of two two-component order parameters. This invariant is the antisymmetric product of the different order parameters and their spatial derivatives. Our theory describes satisfactorily the main features of the behavior of the copper metaborate spin system under applied external magnetic field for the temperature range 2+20 K. The definition of the nature of the low-temperature magnetic state anomalies observed at temperatures near 1.8 K and 1 K requires further consideration. 

While the procedure for this experiment is provided with a fair amount of detail, students can have input into the design of the calorimeter and, although a list of materials is provided, different materials can be made available and they can choose the ones they think would be most effective. The inquiry aspect of this experiment lies primarily in the detailed analysis of their results required to suggest an appropriate interstitial material and the need to assess sources of error. If, for example, students have a large error in the determination of the specific heat capacity of copper, they must decide what could contribute to the error and then try to redesign their calorimeter or their technique in order to limit the error. 

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