# Thread: newton cooling (heating actually) law problem

1. ## newton cooling (heating actually) law problem

A thermometer reading 70 deg F is placed in an oven preheated to a constant temperature through glass window in the oven door, an observer records that the thermometer reads 110 deg F after half min and 145 deg F after one min. how hot is the oven?

answer is 390deg Fahrenheit but i need its detail sloution next week is my seesional plz help me

2. If we indicate with $\displaystyle T(t)$ the measure of the termometer at the time $\displaystyle t$ (expressed in minutes), $\displaystyle T_{0}$ the measure at $\displaystyle t=0$ and $\displaystyle T_{f}$ the (final) measured temperature of the owen we have...

$\displaystyle T=T_{0} + (T_{f} - T_{0}) \cdot (1-e^{- k\cdot t})$ (1)

In (1) there are two unknown parameters, $\displaystyle T_{f}$ (that we want to find) and $\displaystyle k$ (that we probably don't know). If we take into account the measured we have performed at $\displaystyle t=\frac{1}{2}$ and $\displaystyle t=1$ we write...

$\displaystyle T(\frac{1}{2})= T_{0} + (T_{f} - T_{0}) \cdot (1-e^{- \frac{k}{2}})$

$\displaystyle T(1)= T_{0} + (T_{f} - T_{0}) \cdot (1-e^{- k})$ (2)

In (2) you have two equations in two unknown parameters, so you can solve it and find the requested $\displaystyle T_{f}$...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$