# ODE question?

The initial temperature of an object is 5 °C. Then, the object is introduced into a solar oven. It is observed that the rate of change of the object's temperature (°C) in time is proportional to the difference between the object's temperature and the oven's temperature T oven (°C). After 1 hour, the temperature of the object is measured at 21 °C. If the temperature of the oven is T oven = 30°C, how long will it take for the object to have a temperature of 25 °C? You must begin your solution process by writing the differential equation. Use the log chart provided in A.14. Show units in your final answer. Your work must support your answer.

Relevance
• This is a mathematical construct rather than physics.

the initial equation is d (T0- T) /dt = k (T0-T) Where T0 is the fixed temperature of the oven ( 30C)  You can use the exponential substitution to solve.  (T0 - T) = A e^ - bt  Substitute this to find the coefficients of a and b

ie initially at t= 0 the temperature differential is 25  So To-T = 25 e^-bt

at t = 1hour T0-T = 9

so 25 e^-b = 9   Take the natural log of both sides to find b  and then continue.

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