5. You are cooling a dish that was taken out of the oven with an internal temperature of 180°F. After 10 minutes outside in a 70°F apartment, the temperature of the dish has reached 160°F. (a) Using Newton's Law of Cooling, set up a differential equation and show why temperature y of the dish after t minutes out of the oven, is described by the function y(t) = 70+110ekt where k is the cooling constant (you must find). (b) If the dish is safe to eat at 120°F, use the function in (a) to predict how long it needs to be left outside the oven.
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.
According to Newton's law of cooling, the rate of loss of a body is directly proportional to the difference of the temperatures between the body and its surroundings.
Hence,Mathematically.
OR
Where,
Integrating equation (1),we get
Hence,
where,'C' is constant of integration.
First Boundary Conditions is,
Hence, from equation (2)
Hence,
Second boundary condition is,
hence, from equation (2) and (3)
Solving for 'k',
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