Question

A beaker filled with hot water in a room cools from 70°C to 65°C in t1 minutes, 65°C to 60 in
t2minutes and from 60°C to 55°C in t3 minutes. Then,

(b)
t = t = tz
(a)
(c)
< tg <tz
(d)
cannot be concluded​

Answer 1

Answer:

D)

Explanation:

The answer can be found using newton's heat formula

Answer 2

answer whould be t1 < t2 < t3

according to Newton's law of cooling,

-dT/dt ∝ (T - T0) , where To is the temperature of surroundings.

⇒∫-dT/(T - T0) = k∫dt

⇒ln(T1 - T0)/(T2 - T0) = kt

T0 = 25°C [ because beaker filled with hot water in a room and we know, room temperature is 25°C ]

case 1 : T2 = 65 , T1 = 70

now t1 = 1/k ln(65 - 25)/(70 - 25) = 1/k ln(40/45) = 1/k ln(0.889)

case 2 : T2 = 60, T1 = 65

now t2 = 1/k ln(60 - 25)/(65 - 25) = 1/k ln(35/40) = 1/k ln(0.875)

case 3 : T2 = 55 , T1 = 60

now t3 = 1/k ln(55 - 25)/(60 - 25) = 1/k ln(30/35) = 1/k ln(0.85714)

here it is clear that, ln(0.889) < ln(0.875) < ln(0.85714)

hence, t1 < t2 < t3

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