There are two spherical balls $A$ and $B$ of the same material with same surface, but the diameter of $A$ is half that of $B$. If $A$ and $B$ are heated to the same temperature and then allowed to cool, then
Medium
Download our app for free and get started
(c) Rate of cooling ${R_C} = \frac{{A\varepsilon \sigma ({T^4} - T_0^4)}}{{mc}}$$ = \frac{{A\varepsilon \sigma ({T^4} - T_0^4)}}{{V\rho C}}$
==> ${R_C} \propto \frac{A}{V} \propto \frac{1}{r} \propto \,\frac{1}{{({\rm{Diameter)}}}}$ $(\because \,m = \rho V)$
Since diameter of $A$ is half that of $B $ so it's rate of cooling will be doubled that of B
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A liquid cools from $50^oC$ to $45^oC$ in 5 minutes and from $45 ^o C$ to $41.5 ^o C$ in the next $5$ minutes. The temperature of the surrounding is ...... $^oC$View Solution
- 2View SolutionWhich of the following is best close to an ideal black body
- 3Two rectangular blocks $A$ and $B$ of different metals have same length and same area of cross-section. They are kept in such a way that their cross-sectional area touch each other. The temperature at one end of $A$ is $100°C$ and that of $B$ at the other end is $0°C$ . If the ratio of their thermal conductivity is $1 : 3$ , then under steady state, the temperature of the junction in contact will be ........ $^oC$View Solution
- 4The ratio of the diameters of two metallic rods of the same material is $2 : 1$ and their lengths are in the ratio $1 : 4$ . If the temperature difference between their ends are equal, the rate of flow of heat in them will be in the ratioView Solution
- 5A body takes $10$ minutes to cool down from $62^o C$ to $50^o C$. If the temperature of surrounding is $26^o C$ then in the next $10$ minutes temperature of the body will be ......... $^oC$View Solution
- 6The filament of a light bulb has surface area $64 mm ^2$. The filament can be considered as a black body at temperature $2500 K$ emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of $100 m$. Assume the pupil of the eyes of the observer to be circular with radius $3 mm$. ThenView Solution
(Take Stefan-Boltzmann constant $=5.67 \times 10^{-8} Wm ^{-2} K ^{-4}$, Wien's displacement constant $=2.90 \times 10^{-3} m - K$, Planck's constant $=6.63 \times 10^{-34} Js$, speed of light in vacuum $=3.00 \times 10^8 ms ^{-1}$ )-
$(A)$ power radiated by the filament is in the range $642 W$ to $645 W$
$(B)$ radiated power entering into one eye of the observer is in the range $3.15 \times 10^{-8} W$ to $3.25 \times 10^{-8} W$
$(C)$ the wavelength corresponding to the maximum intensity of light is $1160 nm$
$(D)$ taking the average wavelength of emitted radiation to be $1740 nm$, the total number of photons entering per second into one eye of the observer is in the range $2.75 \times 10^{11}$ to $2.85 \times 10^{11}$
- 7A metallic prong consists of $4$ rods made of the same material, cross-sections and same lengths as shown below. The three forked ends are kept at $100^{\circ} C$ and the handle end is at $0^{\circ} C$. The temperature of the junction is ............. $^{\circ} C$View Solution
- 8Assuming the Sun to be a spherical body of radius $R$ at a temperature of $T\ K$, evaluate the total radiant powerd incident of Earth at a distance $r$ from the SunView Solution
Where $r_{0}$ is the radius of the earth and $\sigma$ is Stefan's constant.
- 9One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$ . The rod is composed of two sections of length $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two section isView Solution
- 10View SolutionWoollen clothes are used in winter season because woolen clothes