A body takes 5 text{ min} to cool from 80^{ci | vedclass

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

Question

(B) According to Newton's law of cooling,the rate of cooling is given by $\frac{dT}{dt} = K(T_{avg} - T_{room})$.In the first case,the body cools from

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(B) According to Newton's law of cooling,the rate of cooling is given by $\frac{dT}{dt} = K(T_{avg} - T_{room})$.In the first case,the body cools from $80^{\circ}C$ to $50^{\circ}C$ in $5 	ext{ min}$.$\frac{80 - 50}{5} = K \left( \frac{80 + 50}{2} - 20 ight)$$\frac{30}{5} = K(65 - 20) \implies 6 = 45K \implies K = \frac{6}{45} = \frac{2}{15} \dots (i)$In the second case,the body cools from $60^{\circ}C$ to $30^{\circ}C$ in $t 	ext{ min}$.$\frac{60 - 30}{t} = K \left( \frac{60 + 30}{2} - 20 ight)$$\frac{30}{t} = K(45 - 20) \implies \frac{30}{t} = 25K \dots (ii)$Dividing equation $(i)$ by $(ii)$:$\frac{6}{30/t} = \frac{45K}{25K}$$\frac{6t}{30} = \frac{45}{25}$$\frac{t}{5} = \frac{9}{5}$$t = 9 	ext{ min}$.

$A$ body takes $5 \text{ min}$ to cool from $80^{\circ}C$ to $50^{\circ}C$. How many minutes will it take to cool from $60^{\circ}C$ to $30^{\circ}C$,if the room temperature is $20^{\circ}C$?

Similar Questions

$A$ solid sphere and a hollow sphere of the same material and size are heated to the same temperature and allowed to cool in the same surroundings. If the temperature difference between each sphere and its surroundings is $T$,then

$A$ solid sphere of radius $R$ and a hollow sphere of inner radius $r$ and outer radius $R$ made of copper are heated to the same temperature and are allowed to cool in the same environment. Then,choose the $CORRECT$ statement.

Two circular discs $A$ and $B$ with equal radii and equal mass are blackened. They are heated to the same temperature and are cooled under identical conditions. What inference do you draw from their cooling curves?

$A$ beaker full of hot water is kept in a room. If it cools from $80^{\circ} C$ to $75^{\circ} C$ in $t_1$ minutes,from $75^{\circ} C$ to $70^{\circ} C$ in $t_2$ minutes,and from $70^{\circ} C$ to $65^{\circ} C$ in $t_3$ minutes,then:

$A$ body takes $4$ minutes to cool from $100^{\circ}C$ to $70^{\circ}C$. To cool from $70^{\circ}C$ to $40^{\circ}C$ it will take ........ $\text{min.}$ (room temperature is $15^{\circ}C$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module