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

- 5 °C

Step-by-step 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