Question

A body cools from 60°C to 40°C in 6 minutes. After next 6 minutes its temperature will be (Temperature of the surroundings is 10°C) ______.

Options

• 24°C

• 28°C

• 18°C

• 32°C

Answer 1

A body cools from 60°C to 40°C in 6 minutes. After next 6 minutes its temperature will be (Temperature of the surroundings is 10°C) 28°C.

Explanation:

According to Newton's law of cooling,

\[\frac{\theta_1-\theta_2}{\mathrm{t}}=\mathrm{K}\left[\frac{\theta_1+\theta_2}{2}-\theta_0\right]\]

where, θ₀ = temperature of surrounding

\[\therefore\] \[\frac {60 - 40}{6}\] = K\[\left[{\frac{60+40}{2}}-10\right]\]

\[\frac {20}{6}\] = K × 40   ...(i)

K = \[\frac {1}{12}\]

After another t min, let the temperature be x.

\[\therefore\]\[\frac{40-\mathrm{x}}{6}=\frac{1}{12}\left[\frac{40+\mathrm{x}}{2}-10\right]\]   ...[using (i)]

\[\therefore\] 40 - x = \[\frac {20+x}{4}\]

\[\therefore\] 160 - 4x = 20 + x

\[\therefore\] 5x = 140

\[\therefore\] x = \[\frac {140}{5}\] = 28 °C