If a body is heated to 110^{circ} C and place | vedclass

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

Question

(C) According to Newton's Law of Cooling,$\frac{dT}{dt} = -K(T - T_s)$,where $T_s = 10^{\circ} C$ is the surrounding temperature.Integrating this,we g

Vedclass · Accepted Answer

$\left(\frac{\log 5}{\log 2}-1ight) 	ext{ hrs}$

Vedclass · Answer

(C) According to Newton's Law of Cooling,$\frac{dT}{dt} = -K(T - T_s)$,where $T_s = 10^{\circ} C$ is the surrounding temperature.Integrating this,we get $T(t) = T_s + (T_0 - T_s)e^{-Kt}$.Given $T_0 = 110^{\circ} C$ and $T_s = 10^{\circ} C$,the equation becomes $T(t) = 10 + 100e^{-Kt}$.At $t = 1 	ext{ hour}$,$T = 60^{\circ} C$:$60 = 10 + 100e^{-K(1)} \Rightarrow 50 = 100e^{-K} \Rightarrow e^{-K} = \frac{1}{2} \Rightarrow K = \log 2$.Now,we find the total time $t$ required to reach $T = 30^{\circ} C$:$30 = 10 + 100e^{-(\log 2)t} \Rightarrow 20 = 100e^{-(\log 2)t} \Rightarrow \frac{1}{5} = e^{-(\log 2)t}$.Taking the natural logarithm on both sides:$-\log 5 = -(\log 2)t \Rightarrow t = \frac{\log 5}{\log 2}$.The additional time required is $t - 1 = \frac{\log 5}{\log 2} - 1 	ext{ hours}$.

If a body is heated to $110^{\circ} C$ and placed in air at $10^{\circ} C$,and after $1 \text{ hour}$ its temperature is $60^{\circ} C$,then the additional time required for it to cool to $30^{\circ} C$ is

Similar Questions

If the surrounding air is kept at $25^{\circ} C$ and a body cools from $80^{\circ} C$ to $50^{\circ} C$ in $30 \text{ minutes}$,then the temperature of the body after one hour will be

The bacteria increases at a rate proportional to the number of bacteria present. If the original number $N$ doubles in $4$ hours,then the number of bacteria in $12$ hours will be: (in $N$)

Find the equation of a curve passing through the point $(0,0)$ and whose differential equation is $y^{\prime}=e^{x} \sin x$.

The rate of reduction of a person's assets is proportional to the square root of their existing assets at that moment. If the assets at the beginning are $10000$ and they dwindle down to $5625$ in $2$ years, then the person will be bankrupt in: (in $years$)

The solution of $\frac{dy}{dx} = \frac{ax + b}{cy + d}$ represents a parabola if

Vedclass Test Series

Exam Paper Generator

Online Exam Module