34 STUDIES ON FRUIT RESPIRATION. 



FORMULA FOR CALCULATING RATE OF HEAT ACCUMULATION. 



To determine the amount of heat generated in respiration, it is 

 necessary to know the thermal equivalent of the carbon dioxid 

 formed, which has been assumed to result from the combustion of 

 sucrose, which produces 3.96 calories per gram, when burned com- 

 pletely, in the respiration calorimeter. 1 As the reaction expressing 

 the combustion is 



C 12 H 22 O n + 12 2 = 12 C0 2 + 1 1 H 2 0, 

 342.176 + 384 = 528 + 198.176, 

 each gram of carbon dioxid is accompanied by the evolution of 



342.176X3.96 K ™, , . 2 

 ^ = 2.5663 large calories. 2 



To determine the temperature rise, K, of 1 kilogram of fruit for each 

 gram of carbon dioxid formed, it is necessary to divide by the specific 

 heat of the fruit. Assuming the same specific heat of fruit to be 

 that used by refrigeration engineers, 0.9, iT=2.85° C. and Jc (the tem- 

 perature rise per milligram of carbon dioxid) =0.00285° C. 



Equation 1 (log y = log y + at) expressing the relation between the 

 respiratory activity and the temperature (see p. 20) may be written 



y*=y l<K (2) 



in which y t arid y are the rates of evolution of carbon dioxid per kilo- 

 gram of fruit per hour at t° and at 0°, respectively, and a is a constant 

 determined experimentally. Let the time expressed in hours during 

 which the adiabatic conditions are imposed = T. 



During the first finite interval of time AT, e. g., during the first 

 hour after adiabatic conditions are imposed, the activity is approxi- 

 mately expressed by equation 2 and the temperature rise by 



Jt = Tcy = fcy o 10<* (3) 



the carbon dioxid per kilogram per hour being expressed in milli- 

 grams. As the temperature changes slightly during the first hour 

 in accordance with equation 3, the results are not quite correct. 

 The rate at which the temperature rises at the beginning of the 

 interval AT is evidently correctly expressed by equation 3. 



Therefore dt 7 1 _ , 



jj,= lcy o 10 at . 



On integrating, T=^~ / 10~ at dt= - 



Jcy / lcy a \og e 10 



t> 



lO-at'-lQ-at" 



IQ-at 

 V 



ley a\og e 10 



i Data from U. S. Dept. Agr., Office of Experiment Stations, Bui. 109, p. 17. 



2 The value 2.56 is given as the calorific equivalent of 1 gram of carbon dioxid by Benedict and Car- 

 penter (Carnegie Institution of Washington, No. 126, p. 211). 



