A body cools from 60^{circ} C to 40^{circ} C | 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 proportional to the difference in temperature between the body and its surroundings: $

Vedclass · Accepted Answer

$28$

Vedclass · Answer

(A) According to Newton's law of cooling,the rate of cooling is proportional to the difference in temperature between the body and its surroundings: $\frac{dT}{dt} = -k(T - T_s)$.For the first interval of $6$ minutes:$\frac{60 - 40}{6} = k \left( \frac{60 + 40}{2} - 10 \right)$$\frac{20}{6} = k(50 - 10) = 40k$  --- $(i)$For the next $6$ minutes,let the final temperature be $T$:$\frac{40 - T}{6} = k \left( \frac{40 + T}{2} - 10 \right)$$\frac{40 - T}{6} = k \left( \frac{40 + T - 20}{2} \right) = k \left( \frac{20 + T}{2} \right)$ --- $(ii)$Dividing equation $(i)$ by equation $(ii)$:$\frac{20 / 6}{(40 - T) / 6} = \frac{40k}{k(20 + T) / 2}$$\frac{20}{40 - T} = \frac{80}{20 + T}$$20(20 + T) = 80(40 - T)$$400 + 20T = 3200 - 80T$$100T = 2800$$T = 28^{\circ} C$.

$A$ body cools from $60^{\circ} C$ to $40^{\circ} C$ in $6$ minutes. If the temperature of the surroundings is $10^{\circ} C$,then after the next $6$ minutes,its temperature will be $.........{ }^{\circ} C$.

Similar Questions

$A$ cup of tea cools from $80\,^{\circ}C$ to $60\,^{\circ}C$ in $1$ minute. The ambient temperature is $30\,^{\circ}C$. How long will it take to cool from $60\,^{\circ}C$ to $50\,^{\circ}C$?

For a system where Newton's law of cooling is applicable,the initial rate of cooling is $R \ ^\circ C/sec$. Find the time when the temperature difference $\Delta T_0$ (initial temperature difference) is reduced to half.

Two metal spheres,one solid and one hollow,are heated to $300^{\circ}C$ and allowed to cool in the same environment. The rate of heat loss will be:

$A$ bowl filled with very hot soup cools from $98^{\circ}C$ to $86^{\circ}C$ in $2$ minutes when the room temperature is $22^{\circ}C$. How many minutes will it take to cool from $75^{\circ}C$ to $69^{\circ}C$?

The rates of cooling of two different liquids put in exactly similar calorimeters and kept in identical surroundings are the same if

Vedclass Test Series

Exam Paper Generator

Online Exam Module