Question

A thermometer is taken from a room where the temperature is 21oC21oC to the outdoors, where the temperature is −5oC−5oC. After one minute the thermometer reads 10oC10oC. (a) What will the reading on the thermometer be after 33 more minutes?

Answer 1

Answer:

- 5 °C

Explanation:

$T_{s}$ = Surrounding temperature = - 5 °C

$T(t)$ = temperature at any time "t"

As per newton's law

$T(t) = T_{s} + C e^{kt}$

at t = 0

$T(0) = - 5 + C e^{k(0)}$

$21 = - 5 + C e^{k(0)}$

C = 26

at t = 1

$T(1) = - 5 + (26) e^{k}$

$10 = - 5 + (26) e^{k}$

k = - 0.55

at t = 34

$T(t) = T_{s} + C e^{kt}$

$T(34) = - 5 + (26) e^{34(- 0.55)}$

$T(34)$ = - 5 °C