A cup of coffee cools from 90^{circ} C to 80^ | vedclass

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

Question

(A) Using the average form of Newton's law of cooling: $\frac{dT}{dt} = k(T_{avg} - T_{room})$.For the first interval ($90^{\circ} C$ to $80^{\circ} C

Vedclass · Accepted Answer

$\frac{13}{5} t$

Vedclass · Answer

(A) Using the average form of Newton's law of cooling: $\frac{dT}{dt} = k(T_{avg} - T_{room})$.For the first interval ($90^{\circ} C$ to $80^{\circ} C$):$\frac{90-80}{t} = k\left(\frac{90+80}{2} - 20ight) \implies \frac{10}{t} = k(85 - 20) = 65k \dots (i)$For the second interval ($80^{\circ} C$ to $60^{\circ} C$):$\frac{80-60}{t'} = k\left(\frac{80+60}{2} - 20ight) \implies \frac{20}{t'} = k(70 - 20) = 50k \dots (ii)$Dividing equation $(i)$ by $(ii)$:$\frac{10/t}{20/t'} = \frac{65k}{50k}$$\frac{10}{t} 	imes \frac{t'}{20} = \frac{65}{50}$$\frac{t'}{2t} = \frac{13}{10}$$t' = \frac{13}{10} 	imes 2t = \frac{13}{5} t$.

$A$ cup of coffee cools from $90^{\circ} C$ to $80^{\circ} C$ in $t$ minutes when the room temperature is $20^{\circ} C$. The time taken by the similar cup of coffee to cool from $80^{\circ} C$ to $60^{\circ} C$ at the same room temperature is $:$

Similar Questions

$A$ body cools from $50.0^{\circ}C$ to $49.9^{\circ}C$ in $5\;s$. How long will it take to cool from $40.0^{\circ}C$ to $39.9^{\circ}C$? Assume the temperature of surroundings to be $30.0^{\circ}C$ and Newton's law of cooling to be valid. The time taken is ....... $s$.

$A$ solid sphere and a hollow sphere of the same material and same radius are heated to the same temperature. They are placed in an environment of the same temperature. If the temperature difference between both and the surroundings is $T$,then .......

$A$ 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 $.....^{\circ}C$.

Newton's law of cooling holds good only if the temperature difference between the body and the surroundings is

Vedclass Test Series

Exam Paper Generator

Online Exam Module