A metallic sphere cools from 50^{circ}C to 40 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) According to Newton's Law of Cooling,the rate of cooling is given by $\frac{dT}{dt} = -k(T - T_s)$,where $T_s$ is the surrounding temperature.For

Vedclass · Accepted Answer

$33$

Vedclass · Answer

(A) According to Newton's Law of Cooling,the rate of cooling is given by $\frac{dT}{dt} = -k(T - T_s)$,where $T_s$ is the surrounding temperature.For the first interval: $\frac{50 - 40}{300} = k \left( \frac{50 + 40}{2} - 20 \right)$.$\frac{10}{300} = k(45 - 20) \implies \frac{1}{30} = 25k \implies k = \frac{1}{750}$.For the next $5$ minutes $(300 \, s)$,let the final temperature be $T$. Then: $\frac{40 - T}{300} = k \left( \frac{40 + T}{2} - 20 \right)$.Substituting $k = \frac{1}{750}$: $\frac{40 - T}{300} = \frac{1}{750} \left( \frac{40 + T - 40}{2} \right)$.$\frac{40 - T}{300} = \frac{T}{1500}$.$5(40 - T) = T \implies 200 - 5T = T \implies 6T = 200$.$T = \frac{200}{6} \approx 33.33^{\circ}C$. The closest integer value is $33^{\circ}C$.

$A$ metallic sphere cools from $50^{\circ}C$ to $40^{\circ}C$ in $300 \, s$. If the atmospheric temperature is $20^{\circ}C$,then the sphere's temperature after the next $5$ minutes will be close to $.....^{\circ}C$.

Similar Questions

$A$ certain quantity of water cools from $70^\circ C$ to $60^\circ C$ in the first $5$ minutes and to $54^\circ C$ in the next $5$ minutes. The temperature of the surroundings is ..... $^\circ C$

If a body cools from a temperature of $62^{\circ} C$ to $50^{\circ} C$ in $10 \, \text{minutes}$ and to $42^{\circ} C$ in the next $10 \, \text{minutes}$, then the temperature of the surroundings is (in $^{\circ} C$)

$A$ body cools from $60^{\circ}C$ to $50^{\circ}C$ in $10$ minutes. If the room temperature is $25^{\circ}C$ and Newton's law of cooling is applicable,what will be the temperature of the body after another $10$ minutes in $^{\circ}C$?

$A$ bucket full of hot water cools from $75^{\circ}C$ to $70^{\circ}C$ in time $T_1$,from $70^{\circ}C$ to $65^{\circ}C$ in time $T_2$,and from $65^{\circ}C$ to $60^{\circ}C$ in time $T_3$. Which of the following relations is correct?

$A$ body cools from $60\,^oC$ to $50\,^oC$ in $10\, minutes$. If the room temperature is $25\,^oC$ and assuming Newton's law of cooling to hold good,the temperature of the body at the end of the next $10\, minutes$ will be ....... $^oC$

Vedclass Test Series

Exam Paper Generator

Online Exam Module