A liquid cools from 50^{circ}C to 45^{circ}C | vedclass

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

Question

(D) According to Newton's law of cooling,the rate of cooling is proportional to the difference between the average temperature of the liquid and the s

Vedclass · Accepted Answer

$33.3$

Vedclass · Answer

(D) According to Newton's law of cooling,the rate of cooling is proportional to the difference between the average temperature of the liquid and the surrounding temperature:$\frac{T_1 - T_2}{t} = K \left( \frac{T_1 + T_2}{2} - T_0 \right)$For the first interval ($50^{\circ}C$ to $45^{\circ}C$ in $5 \ minutes$):$\frac{50 - 45}{5} = K \left( \frac{50 + 45}{2} - T_0 \right)$$1 = K (47.5 - T_0) \quad \dots (i)$For the second interval ($45^{\circ}C$ to $41.5^{\circ}C$ in $5 \ minutes$):$\frac{45 - 41.5}{5} = K \left( \frac{45 + 41.5}{2} - T_0 \right)$$0.7 = K (43.25 - T_0) \quad \dots (ii)$Dividing equation $(i)$ by $(ii)$:$\frac{1}{0.7} = \frac{47.5 - T_0}{43.25 - T_0}$$43.25 - T_0 = 0.7(47.5 - T_0)$$43.25 - T_0 = 33.25 - 0.7T_0$$0.3T_0 = 10$$T_0 = \frac{10}{0.3} = 33.33^{\circ}C$Thus,the surrounding temperature is approximately $33.3^{\circ}C$.

$A$ liquid cools from $50^{\circ}C$ to $45^{\circ}C$ in $5 \ minutes$ and from $45^{\circ}C$ to $41.5^{\circ}C$ in the next $5 \ minutes$. The temperature of the surrounding is ......... $^{\circ}C$.

Similar Questions

The uncertainties in the velocities of two particles $A$ and $B$ are $0.05 \ m/s$ and $0.02 \ m/s$ respectively. The mass of $B$ is five times that of mass $A$. What is the ratio of uncertainties $\left(\frac{\Delta x_A}{\Delta x_B}\right)$ in their positions?

Let $f(x)$ be a polynomial of degree $3$ such that $f(-1) = 10$,$f(1) = -6$,$f(x)$ has a critical point at $x = -1$,and $f'(x)$ has a critical point at $x = 1$. Then $f(x)$ has a local minima at $x =$

$ICBN$ stands for

What is the undifferentiated mass of cells in tissue culture called?

Which among the following is a non-reducing sugar?

Vedclass Test Series

Exam Paper Generator

Online Exam Module