Suppose coffee has a temperature of 200 degrees F when freshly poured, and the room temperature is 72 degrees F. In this exercise use Newton's law of cooling, that is, the rate of change of the temperature of an object is proportional to the difference between its temperature and the ambient temperature, which can be written as dT/dt = -k(T-Ta). (a) What IVP does the temperature of the coffee satisfy? (b) What is the solution of the IVP? (c) If the coffee cools to 136 degrees F in five minutes, what is the value of k? (d) When does the coffee reach a temperature of 150 degrees F?
Energy transfer
The flow of energy from one region to another region is referred to as energy transfer. Since energy is quantitative; it must be transferred to a body or a material to work or to heat the system.
Molar Specific Heat
Heat capacity is the amount of heat energy absorbed or released by a chemical substance per the change in temperature of that substance. The change in heat is also called enthalpy. The SI unit of heat capacity is Joules per Kelvin, which is (J K-1)
Thermal Properties of Matter
Thermal energy is described as one of the form of heat energy which flows from one body of higher temperature to the other with the lower temperature when these two bodies are placed in contact to each other. Heat is described as the form of energy which is transferred between the two systems or in between the systems and their surrounding by the virtue of difference in temperature. Calorimetry is that branch of science which helps in measuring the changes which are taking place in the heat energy of a given body.
Suppose coffee has a temperature of 200 degrees F when freshly poured, and the room temperature is 72 degrees F. In this exercise use Newton's law of cooling, that is, the rate of change of the temperature of an object is proportional to the difference between its temperature and the ambient temperature, which can be written as dT/dt = -k(T-Ta).
(a) What IVP does the temperature of the coffee satisfy?
(b) What is the solution of the IVP?
(c) If the coffee cools to 136 degrees F in five minutes, what is the value of k?
(d) When does the coffee reach a temperature of 150 degrees F?
Given information:
The initial temperature of the coffee (T0) = 2000 F
The ambient temperature (Ta) = 720 F
The rate of change of temperature is given as:
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