newton cooling (heating actually) law problem

**eaglepk1125** · March 21st 2009, 11:47 PM

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

**chisigma** · March 26th 2009, 05:31 AM

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

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

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

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

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

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

Kind regards

$\chi$ $\sigma$

Thread: newton cooling (heating actually) law problem

LinkBack

Thread Tools

Display

newton cooling (heating actually) law problem

Similar Math Help Forum Discussions

Newton's Law of Heating/Cooling

Newton's law of cooling vs heating URGENT!

Heating and Cooling of Buildings

help with DE problem: Newton's law of cooling

Newton's law of Heating and Cooling

Search Tags