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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?

Respuesta :

Answer:

- 5 °C

Explanation:

[tex]T_{s}[/tex] = Surrounding temperature = - 5 °C

[tex]T(t) [/tex] = temperature at any time "t"

As per newton's law

[tex]T(t) = T_{s} + C e^{kt}[/tex]

at t = 0

[tex]T(0) = - 5 + C e^{k(0)}[/tex]

[tex]21 = - 5 + C e^{k(0)}[/tex]

C = 26

at t = 1

[tex]T(1) = - 5 + (26) e^{k}[/tex]

[tex]10 = - 5 + (26) e^{k}[/tex]

k = - 0.55

at t = 34

[tex]T(t) = T_{s} + C e^{kt}[/tex]

[tex]T(34) = - 5 + (26) e^{34(- 0.55)}[/tex]

[tex]T(34)[/tex] = - 5 °C

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