(1 pt) A thermometer is taken from a room where the temperature is 23 o C to the

Question

(1 pt) A thermometer is taken from a room where the temperature is 23oC to the outdoors, where the temperature is 0oC. After one minute the thermometer reads 16oC.
(a) What will the reading on the thermometer be after 2 more minutes?
,
(b) When will the thermometer read 1oC?
minutes after it was taken to the outdoors.
(1 pt) A thermometer is taken from a room where the temperature is 23oC to the outdoors, where the temperature is 0oC. After one minute the thermometer reads 16oC.
(a) What will the reading on the thermometer be after 2 more minutes?
,
(b) When will the thermometer read 1oC?
minutes after it was taken to the outdoors.

Explanation / Answer

Ts is surrounding temperature

T is the current temperature

then we have dT/dt (time derivative) = k (Ts - T) where k is a constant; this is Newton's Law of cooling.

Using this we find,

ln{ (T2 - Ts)/(T1 - Ts) } = -k (t2 - t1) where t repesents temperature, t represents time of the initial and final states 1 and 2 respectively.

here Ts = 0, T1= 23, T2= 16, t2 - t1 = 1

then k = 0.362905 /min

a. then putting the values of k from above, and Ts=0, T1=23, t2 - t1 = 3 we get T2 = 7.7429

b. then putting T2=1, Ts=0, T1=23, and k from above we get t2 - t1 = 8.64min

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.