Two spheres have a radius ratio of 1:2 and a | vedclass

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

Question

(B) According to Stefan-Boltzmann Law,the rate of heat loss is given by $dQ/dt = \sigma A (T^4 - T_0^4)$.For a small temperature difference,the rate o

Vedclass · Accepted Answer

$1:1$

Vedclass · Answer

(B) According to Stefan-Boltzmann Law,the rate of heat loss is given by $dQ/dt = \sigma A (T^4 - T_0^4)$.For a small temperature difference,the rate of cooling $d	heta/dt$ is proportional to the rate of heat loss divided by the heat capacity $(ms)$:$d	heta/dt = \frac{\sigma A (T^4 - T_0^4)}{ms}$.Since $m = ho V = ho (\frac{4}{3}\pi r^3)$ and $A = 4\pi r^2$,we have:$d	heta/dt \propto \frac{r^2}{ho r^3 s} \propto \frac{1}{ho r}$.Given the ratios $r_1:r_2 = 1:2$ and $ho_1:ho_2 = 2:1$,the ratio of the rate of cooling is:$\frac{(d	heta/dt)_1}{(d	heta/dt)_2} = \frac{ho_2 r_2}{ho_1 r_1} = \frac{1}{2} 	imes \frac{2}{1} = 1:1$.

Two spheres have a radius ratio of $1:2$ and a density ratio of $2:1$. They have the same specific heat. If they are heated to the same temperature and placed in the same environment,what is the ratio of their rate of cooling?

Similar Questions

An object is cooled from $75^{\circ}C$ to $65^{\circ}C$ in $2$ minutes in a room at $30^{\circ}C$. The time taken to cool another object from $55^{\circ}C$ to $45^{\circ}C$ in the same room in minutes is

$A$ hollow copper sphere $S$ and a hollow copper cube $C$,both with negligible thin walls of the same surface area,are filled with water at $90^{\circ}C$ and allowed to cool in the same environment. The graph that correctly represents their cooling is:

The rate of cooling at $600 \ K$ is $R$,given the surrounding temperature is $300 \ K$. What is the rate of cooling at $900 \ K$?

$A$ liquid in a beaker has temperature $\theta(t)$ at time $t$ and $\theta_0$ is the temperature of the surroundings. According to Newton's law of cooling,the correct graph between $\log_e(\theta - \theta_0)$ and $t$ is:

For which method of heat transfer can Newton's law of cooling be used?

Vedclass Test Series

Exam Paper Generator

Online Exam Module