A body takes 5 minute for cooling from 50⁰C to 40⁰C. Its temperature

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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.

Related Questions:

1. Consider two nuclei of the same radioactive nuclide. One of the nuclei was created
2. The velocity of a particle at an instant is 10 ms⁻¹ and after 5 s the velocity
3. In nuclear fission, the percentage of mass converted into energy is about
4. Alternating current is transmitted to distant places at
5. Fission of nuclei is possible because the binding energy per nucleon in them

Topics: Properties of Bulk Matter (130)
Subject: Physics (2479)

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