# 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.

### 1 Answer

- Andrew SmithLv 71 month ago
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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