Question

A body cools in $7$ minutes from ${60}^{o}C$ to ${40}^{o}C$. If the temperature of surrounding is ${10}^{o}C$, the temperature after next $7$ minutes will be :

• A. ${32}^{o}C$
• B. ${38}^{o}C$
• C. ${22}^{o}C$
• D. None of these

Answer 1

The correct option is D None of these

From newton's law of cooling

$\frac{dT}{dt}=k(T-T_{surrounding})$...(i)
integrating equation (i)

$\frac{T_f-T_{surrounding}}{T_i-T_{surrounding}}=e^{-kt}$..(ii)
From given data in question in first $7$ minutes $T_f=40C;T_i=60C;T_{surrounding}={10}^{o}C$

$\frac{40-10}{60-10}=e^{-k7},$...(iii)
Now the temperature decrease further due to temperature gradient
From given data in question in next $7$ minutes $T_f=?;T_i=40C;T_{surrounding}={10}^{o}C$
applying equation (i)

$\frac{T_f-10}{40-10}=e^{-k7},$...(iv)
substituting value of $e^{-k7},$ from equation(iii)

$\frac{T_f-10}{40-10}=\frac{3}{5}$

$T_f=10+18={28}^{o}C$
Hence correct option is D