Cooling Curve Analysis: t vs. T Difference

In summary, the conversation discusses the process of measuring the temperature difference between a liquid and its surroundings as it cools over time. The results show that the cooling curve follows the form T = Ae^-kt. To obtain the values of A and k, one could take the natural logarithm of both sides and plot the resulting straight line graph to determine the values through graphical analysis.
  • #1
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When a liquid is cooled, the difference between the temperature of the liquid and the surrondings is measured. The results are:


t(min) 10 20 30 40
T(°C) 60.7 36.8 22.3 13.5


Where t= time from the start of the cooling
T= temperature difference

Q(i) Process the above data and show that the cooling curve has the form:

T=Ae^(-kt)

I'm not sure how to do this. I have gone through the textbook and there are no similar questions to this. The only one close has a different form.
I tried getting a value for A using a computer programme, but it said that there is no algebraic solution. I also tried getting a value for -k that worked but I'm not sure how to transform this data to show a cooling curve.

b) Find the values of A and k.

Thanks for any help.
 
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  • #2
If the data obeys the equation T = Ae-kt, what happens if you take the natural logarithm of both sides?
 
  • #3
Wouldn't this transform it into a straight line ?
 
  • #4
Yes it would. And that makes it a whole lot easier to obtain the value of A and k graphically. Plot the resulting straight line graph with appropriate axes. Then from the gradient and y-intercept, you could get the values you need after some algebraic manipulation.
 

1. What is cooling curve analysis?

Cooling curve analysis is a method used in materials science to study the cooling behavior of a substance. It involves plotting the temperature of the substance over time as it cools, and analyzing the resulting curve to gain insights into the material's properties and behavior.

2. Why is cooling curve analysis important?

Cooling curve analysis is important because it allows scientists to understand the thermal properties of a material, such as its melting point, freezing point, and heat capacity. This information is crucial for a wide range of applications in fields such as engineering, chemistry, and metallurgy.

3. How is cooling curve analysis performed?

To perform cooling curve analysis, a sample of the material is heated to a high temperature and then allowed to cool at a controlled rate. The temperature is continuously measured and recorded, and a graph is created by plotting the temperature against time. This graph, known as a cooling curve, can then be analyzed to determine the material's properties.

4. What factors can affect the cooling curve of a substance?

Several factors can affect the cooling curve of a substance, including its composition, impurities, and thermal conductivity. The rate at which the substance is cooled can also have a significant impact on the resulting curve.

5. What are some practical applications of cooling curve analysis?

Cooling curve analysis has many practical applications, such as in the development of new materials with specific thermal properties, the optimization of industrial processes, and the quality control of manufactured products. It is also used in research to understand the behavior of materials under different conditions.

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