In general, the cooling of a hot steel bar can be described by the following differential equation: dT = a(T- 20) dt %3D where the surrounding room temperature is 20°C and a is a constant that describes how easily heat can transfer between the bar and the environment. Your steel bar has been heated to 200°C and will be allowed to cool from 200°C in such a way that the ODE describes its temperature. The coefficient 'a' describes how quickly heat is dissipated, and is affected by things like insulation or airflow around the bar. You wish to determine the value of 'a' required to allow the bar to cool down to below 30°C within 4 minutes, to the nearest two decimal places. Use a for loop to test all values of the 'a' coefficient between 0 and -1. Use an appropriately high resolution to ensure that your answer converges with the true answer. Answer:
In general, the cooling of a hot steel bar can be described by the following differential equation: dT = a(T- 20) dt %3D where the surrounding room temperature is 20°C and a is a constant that describes how easily heat can transfer between the bar and the environment. Your steel bar has been heated to 200°C and will be allowed to cool from 200°C in such a way that the ODE describes its temperature. The coefficient 'a' describes how quickly heat is dissipated, and is affected by things like insulation or airflow around the bar. You wish to determine the value of 'a' required to allow the bar to cool down to below 30°C within 4 minutes, to the nearest two decimal places. Use a for loop to test all values of the 'a' coefficient between 0 and -1. Use an appropriately high resolution to ensure that your answer converges with the true answer. Answer:
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Transcribed Image Text:In general, the cooling of a hot steel bar can be described by the following differential equation:
dT
= a(T- 20)
dt
%3D
where the surrounding room temperature is 20°C and a is a constant that describes how easily heat can transfer between the bar and the environment.
Your steel bar has been heated to 200°C and will be allowed to cool from 200°C in such a way that the ODE describes its temperature.
The coefficient 'a' describes how quickly heat is dissipated, and is affected by things like insulation or airflow around the bar. You wish to determine the
value of 'a' required to allow the bar to cool down to below 30°C within 4 minutes, to the nearest two decimal places.
Use a for loop to test all values of the 'a' coefficient between 0 and -1. Use an appropriately high resolution to ensure that your answer converges with the
true answer.
Answer:
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