The temperature of a body falls from 40°C to 36°C in 4 minutes when placed in a surrounding of constant temperature 20°C. Its temperature falls further from 36°C to 32°C in the same surrounding in time (Use approximation in newton's law of cooling)

Engineering

Physics

Conduction of Heat

Radiation

Question

The temperature of a body falls from 40°C to 36°C in 4 minutes when placed in a surrounding of constant temperature 20°C. Its temperature falls further from 36°C to 32°C in the same surrounding in time

(Use approximation in newton's law of cooling)

6 min

6.8 min

5.1 min

6.5 min

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Rate of fall of temperature a (θ_av – θ₀) i.e. $\frac{Δθ}{Δt}$ α (θ_av – θ₀)
where θ_av $\overset{}{\to}$ Average temp. of the body = (θ_in + θ_f )/2
θ₀ $\overset{}{\to}$ Temp. of surrounding
$∴ \frac{(\frac{40 - 36}{4})}{(\frac{36 - 32}{t})} = \frac{[(\frac{40 + 36}{2}) - 20]}{[(\frac{36 + 32}{2}) - 20]}$
$∴$ t = 5.1 min