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In an animal obtaining all its energy by the oxidation of glucose, the utilisation of 1 litre of oxygen would lead to production of 673/(6x22.4)=5.007 Kcal of heat, for mixtures of carbohydrates an average value is 5.047 Kcal per litre. Such values are known as thermal equivalents of oxygen, and are used in indirect calorimetry to estimate heat production from oxygen consumption.
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For an animal catabolishing mixtures of fats alone, (of 4.715 Kcal per litre calculated from equation (2) above).
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Animals do not normally obtain energy exclusively from either carbohydrate or fat.
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They oxidise a mixture of these (and of protein also), so that in order to apply the appropriate thermal equivalent when converting oxygen consumption to heat production it is necessary to know how much of the oxygen is used for each nutrient.
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The proportions are calculated from what is known as the respiratory quotient (RQ).
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This is the ratio between the volume of carbon dioxide produced by the animal and the volume of oxygen used.
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Since, under the same conditions of temperature and pressure, equal volumes of gases contain equal numbers of molecules, the RQ can be calculated from the molecules of carbon dioxide produced and oxygen used.
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From equation (1) the RQ for carbohydrate is calculated as 6 Co2/6 O2 = 1, and from equation (2) that of the fat, tripalmitin, as 51 CO2/72.5 O2=0.70.
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If the RQ of an animal is known, the proportions of fat and carbohydrate oxidised can then be determined from standard tables. For example, an RQ of 0.9 indicates the oxidation of a mixture of 67.5% carbohydrate and 32.5% fat, and the thermal equivalent of oxygen for such a mixture is 4.924 Kcal/litre.
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The mixture oxidised generally includes protein.
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The quantity of protein catabolised can be estimated from the output of nitrogen in the urine, 0.16g of urinary N being excreted for each gram of protein.
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The heat of combustion of protein (i.e. the heat produced when it is completely oxidised) varies according to the amino acid proportions but averages 5.3 Kcal per g.
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Protein, however, is incompletely oxidised in animals because the body cannot oxidise nitrogen, and the aveerage amount of heat produced by the catabolism of 1 g. of protein is 4.3 Kcal.
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For each gram of protein oxidised, 0.77 litres of carbondioxide is produced and 0.96 litres of oxygen used, giving an RQ of 0.8.
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In practice heat production calculate from respiratory exchange in ruminants is corrected for this effect by the deduction of 0.5 Kcal for each litre of methane.
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An alternative means of over-coming difficulties of this kind is to calculate heat production from oxygen consumption alone.
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If a respiratory quotient of 0.82 and a thermal equivalent of 4.8 are assumed, departures from this RQ of between 0.7 and 1.0 cause a maximum bias of no more than 3.5% in the estimate of heat production.
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A further simplification is possible in respect of protein metabolism.
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The thermal equivalent of oxygen used for protein oxidation is 4.5 Kcal per litre, not very different from the value of 4.8 assumed for carbohydrate and fat oxidation.
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If only a small proportion of the heat production is caused by protein oxidation it is unnecessary to assess it separately, and so urinary nitrogen output need not be measured.
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An example of the calculation of heat production from respiratory exchange is shown below: