I chose this article with interest in knowing the elaborated process of pasteurization of milk and in turn do the reflection of the concepts learn in class and relate with this article. The idea of equilibrium solution for different equations has got reflected in the article. The technique that I have so far studied in class regarding the concept become mathematical express in the article. The mathematical aspects of the article are related to the idea of equilibrium when it comes to determination of the concentration of bacteria in milk. Notably, the concept of stability of equilibria for differential equations become also reflected in the article. Heating of liquid gets done with the specific amount of time and temperatures. The same has got graphically represented to analyze the data obtained in the experiment. All the graphical methods that became covered in the class got elaborated in the article. (FREEMAN, R. O. W. L. A. N. D. G. O. D. F. R. E. Y. 2017).

Companies would want to achieve quality output with minimum cost. To get this the company has to make a comparison of the various alternative of the solution and take the take the one that yields better results. I will handle on an illustration concerning pasteurization of milk by a company. Milk get usually considered purified when held at a temperature of 150 degrees Celsius for 30 minutes. When the liquid begins heating, it starts at a temperature of 60 degrees Celsius. The heating will continue until when the temperatures of 150 degrees get achieved and would get kept constant for maximum output.

The concept of equilibrium solution gets discussed in detail in the paper. In this case of milk pasteurization, the equilibrium solution is said to have got achieved when the temperatures of 150 degrees Celsius get reached and maintained. In my example, we shall see the scenario where the milk get heated from 60 degrees Celsius to 150 degrees for 30 minutes. To calculate the concentration of bacteria which will remain after boiling the milk for 30 minutes, we will use the derived formulas. (FREEMAN, R. O. W. L. A. N. D. G. O. D. F. R. E. Y. 2017).

The number of bacteria Nt will decay with time t as per the equation below

dNdt=--2.303DTtNt.

In my case, the temperature became fixed at Tt=150 which is D 150=2. It therefore implies that dNdt=-1.1515 and it shows that dNtNt=-1.1515dt. we know that Nt in this system become the function of time.

In Integrating both sides of the equation, the result is as shown below

In(Nt)=-1.1515t+c

Nt= c (e to the power of -1.1515t)

For the constant c. We can get the solution as shown below when t=0 which the above equation will become c=N0

Nt =c (e to the power of -1.1515t)

In the above process, the-the concentration occurs finally at t=30. The natural logarithm therefore of the final to the initial concentration ratio becomes a fixed number as shown below

In NtN0=-1.1515*30=-34.545

The graph below illustrates the heating process from 60 to 150 when the temperature get kept constant.

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Conclusion

In summary, beginning the process of pasteurization from a lower temperature and slowly raising it to full heat takes more time to kill the bacteria than when started at the total heat. The constant temperature of 150 is required and heating of 30 minutes would get a need for better results. Different companies use different methods of pasteurization, and they manage to achieve the same task but at varying cost. Pasteurization does not get done to destroy all the pathogenic microorganisms in liquids or food. The process only gets aims to lower their number to avoid causing diseases.

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Reference

FREEMAN, R. O. W. L. A. N. D. G. O. D. F. R. E. Y. (2017). LOW-TEMPERATURE PASTEURIZATION OF MILK AT ABOUT 68 C (155F) (CLASSIC REPRINT). S.l.: FORGOTTEN BOOKS.

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