Certain quantity of water cools from 70⁰ C to 60⁰C in the first 5 minutes and to 54⁰C

Certain quantity of water cools from 70⁰ C to 60⁰C in the first 5 minutes and to 54⁰ C in the next 5 minutes. The temperature of the surroundings is

Options

(a) 45⁰ C
(b) 20⁰ C
(c) 42⁰ C
(d) 10⁰ C

Correct Answer:

45⁰ C

Explanation:

Let the temperature of surroundings be θ₀
By Newton’s law of cooling
(θ₁ – θ₂ / t) = k [(θ₁ – θ₂ / 2) – θ₀]
[(70 – 60) / 5] = k [(70 + 60 / 2) – θ₀] ⇒ 2 = k [65 – θ₀] ——(i)
Similarly, (60 – 54) / 5 = k = [(60 + 54 / 2) – θ₀]
6 / 5 = k [57 – θ₀] ——–(ii)
By dividing (i) by (ii) we have
10 / 6 = (65 – θ₀) / (57 – θ₀) ⇒ θ₀ = 45⁰

admin:

Related Questions

  1. A particle starts its motion from rest under the action of a constant force
  2. The given graph represents V-I characteristic for a semiconductor device
  3. Length of a conductor is 50 cm radius of cross section 0.1 cm and resistivity
  4. Excitation energy of a hydrogen like ion, in its first excitation state, is 40.8 eV.
  5. Two charged spheres seperated at a distance d exert a force F on each other.