Question 4 [Total 20 marks] The picture on the right shows a steel column tested by one of Prof. Kwon's graduate students in August 2017. The temperature of the column was increased up to 740 °C ina furnace. Then, the furnace was turned off, and the gate of the furnace was opened to let the column cool down. The ambient temperature of the lab was 18 °C. After 2,130 sec since the gate was opened, the temperature of the column decreased to 400 °C. From the time when the gate was opened, how long will it take for the specimen to reach 200 °C? To solve the problem, 1) formulate an ODE assuming that the temperature change of the column follows Newton's law of cooling, 2) find a particular solution of the ODE and predict the time to reach 200 °C of temperature. [Newton's Law of Cooling] The rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e. the temperature of its surroundings) Question 4 [Total 20 marks] The picture on the right shows a steel column tested by one of Prof. Kwon's graduate students in August 2017. The temperature of the column was increased up to 740 °C ina furnace. Then, the furnace was turned off, and the gate of the furnace was opened to let the column cool down. The ambient temperature of the lab was 18 °C. After 2,130 sec since the gate was opened, the temperature of the column decreased to 400 °C. From the time when the gate was opened, how long will it take for the specimen to reach 200 °C? To solve the problem, 1) formulate an ODE assuming that the temperature change of the column follows Newton's law of cooling, 2) find a particular solution of the ODE and predict the time to reach 200 °C of temperature. [Newton's Law of Cooling] The rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e. the temperature of its surroundings)