4. Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature) dT/dt = -k(T - Ta) where T= the temperature of the body (°C), t= time (min). k= the proportionality constant (per minute), and Ta = the ambient temperature (°C). Suppose that a cup of coffee originally has a temperature of 68°C. Use Euler's method to compute the temperature from t=0 to 10 min using a step size of 1 min if Ta =21°C and k= 0.1/min.
4. Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature) dT/dt = -k(T - Ta) where T= the temperature of the body (°C), t= time (min). k= the proportionality constant (per minute), and Ta = the ambient temperature (°C). Suppose that a cup of coffee originally has a temperature of 68°C. Use Euler's method to compute the temperature from t=0 to 10 min using a step size of 1 min if Ta =21°C and k= 0.1/min.
Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Solve the following using the required numerical methods of solution. Show step by step solution , corresponding tables and graph
Transcribed Image Text:4. Newton's law of cooling says that the temperature of a body changes at a rate proportional to the difference between its temperature and that of the surrounding medium (the ambient temperature).
dT/dt = -k(T - Ta)
where T= the temperature of the body (°C),
t= time (min).
k= the proportionality constant (per minute), and
Ta = the ambient temperature (°C).
Suppose that a cup of coffee originally has a temperature of 68°C. Use Euler's method to compute the temperature from t= 0 to 10 min using a step size of 1 min if Ta = 21°C and k= 0.1/min.
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