Thermodynamics Question 11
Question 11 - 29 January - Shift 1
A body cools from $60^{\circ} C$ to $40^{\circ} C$ in 6 minutes. If, temperature of surroundings is $10^{\circ} C$. Then, after the next 6 minutes, its temperature will be ______ ${ }^{\circ} C$.
Show Answer
Answer: (28)
Solution:
Formula: Newton’s law of cooling
By average form of Newton’s law of cooling $$ \begin{aligned} & \frac{20}{6}=\mathrm{k}(50-10) \ & \frac{40-\mathrm{T}}{6}=\mathrm{K}\left(\frac{40+\mathrm{T}}{2}-10\right) \end{aligned} $$
From equation (i) and (ii) $$ \begin{aligned} & \frac{20}{40-\mathrm{T}}=\frac{40}{10+\mathrm{T} / 2} \ & 10+\frac{\mathrm{T}}{2}=80-2 \mathrm{~T} \end{aligned} $$
