Question

A body cools from a temperature $3T$ to $2T$ in $10$ minutes. The room temperature is $T$. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next $10$ minutes will be

• A. $\frac{7}{4}T$
• B. $\frac{3}{2}T$
• C. $\frac{4}{3}T$
• D. $T$

Answer 1

Answer: (B)

$\frac{3}{2}T$

From newton's law of cooling,

$ln\left(\frac{3T-T}{2T-T}\right)=kt$

$=ln\left(2\right)=k\left(10\right)$

For next 10 minutes,

$ln\left(\frac{2T-T}{T^{\prime }-T}\right)=k\left(10\right)$

$⟹\frac{2T-T}{T^{\prime }-T}=2$

$⟹T^{\prime }=\frac{3}{2}T$