A solid cube and a solid sphere of identical | vedclass

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

Question

(B) According to Newton's law of cooling,the rate of heat loss $dQ/dt$ is proportional to the surface area $A$ of the body,i.e.,$dQ/dt \propto A$.For

Vedclass · Accepted Answer

the cube will cool faster because it has a larger surface area

Vedclass · Answer

(B) According to Newton's law of cooling,the rate of heat loss $dQ/dt$ is proportional to the surface area $A$ of the body,i.e.,$dQ/dt \propto A$.For a given mass $m$ and density $\rho$,the volume $V = m/\rho$ is the same for both the cube and the sphere.Since the volume of a sphere is $V = (4/3)\pi r^3$ and the volume of a cube is $V = a^3$,the surface area of the cube $(6a^2)$ is greater than the surface area of the sphere $(4\pi r^2)$ for the same volume.Because the cube has a larger surface area,it loses heat at a faster rate than the sphere.Additionally,sharp edges on the cube facilitate more effective radiation compared to a smooth spherical surface.Therefore,the cube cools faster than the sphere. Thus,option $(b)$ is correct.

$A$ solid cube and a solid sphere of identical material and equal masses are heated to the same temperature and left to cool in the same surroundings. Then,

Similar Questions

$A$ solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature $120^{\circ}C$,then

If a liquid cools from $95^{\circ}C$ to $90^{\circ}C$ in $30 \, s$ and from $55^{\circ}C$ to $50^{\circ}C$ in $70 \, s$,then the temperature of the surroundings is ...... $^{\circ}C$. (in $.5$)

The circuit below is used to heat water kept in a bucket. Assuming heat loss only by Newton's law of cooling, the variation in the temperature of the water in the bucket as a function of time is depicted by

The temperature of a liquid falls from $365 \, K$ to $359 \, K$ in $3 \, minutes$. The time during which the temperature of this liquid falls from $342 \, K$ to $338 \, K$ is [Let the room temperature be $296 \, K$] (in $min$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module