A body takes 5 minute for cooling from 50⁰C to 40⁰C. Its temperature comes down to 33.33⁰C in next 5 minute. Temperature of surroundings is

Options

(a) 15⁰C
(b) 20⁰C
(c) 25⁰C
(d) 10⁰C

Correct Answer:

20⁰C

Explanation:

Apply Newton’s law of cooling
In first case, (50 – 40)/5 = K [(50+40)/2 – θ]
⇒ 2 = K [45 – θ] ——(i)
In second case, take 33.33 = 33 x (1/3) = 100/3
[40 – (100/3)]/5 = K {[40 + (100/3)/2] – θ}
⇒ 20/(5×3) = K [(110/3) – θ] ——(ii)
(i)/(ii) = (2 x 5 x 3)/20 = (45 – θ) / [(110/3) – θ]
⇒ 3/2 = (45 – θ) / [(110/3) – θ]
= 110 – 30 = 90 – 20 ⇒ θ = 20⁰C.