A sphere is at temperature 600 K. In an exte | vedclass

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

Question

(A) According to Stefan-Boltzmann Law,the rate of cooling $R$ of a body at temperature $T$ in an environment at temperature $T_0$ is given by: $R = e

Vedclass · Accepted Answer

$\frac{3}{16} R$

Vedclass · Answer

(A) According to Stefan-Boltzmann Law,the rate of cooling $R$ of a body at temperature $T$ in an environment at temperature $T_0$ is given by: $R = e \sigma A (T^4 - T_0^4)$ For the first case,$T = 600 \ K$ and $T_0 = 200 \ K$: $R = k (600^4 - 200^4)$ For the second case,$T' = 400 \ K$ and $T_0 = 200 \ K$: $R' = k (400^4 - 200^4)$ Taking the ratio: $\frac{R'}{R} = \frac{400^4 - 200^4}{600^4 - 200^4} = \frac{(4^4 - 2^4) 	imes 10^8}{(6^4 - 2^4) 	imes 10^8}$ $\frac{R'}{R} = \frac{256 - 16}{1296 - 16} = \frac{240}{1280} = \frac{24}{128} = \frac{3}{16}$ Therefore,$R' = \frac{3}{16} R$.

$A$ sphere is at temperature $600 \ K$. In an external environment of $200 \ K$,its cooling rate is $R$. When the temperature of the sphere falls to $400 \ K$,then the cooling rate $R'$ will become:

Similar Questions

$A$ container has a small hole. At what temperature (in $K$) should it be maintained so that it emits $1 \ cal$ of energy per second per $m^2$?

The temperature of a body is increased from $-73^{\circ}C$ to $327^{\circ}C$. The ratio of energy emitted per second is:

If the radiation emitted by a perfect radiator has maximum intensity at a wavelength of $2900 Å$, the intensity of radiation emitted by it is (Stefan-Boltzmann's constant $= 5.67 \times 10^{-8} W m^{-2} K^{-4}$ and Wien's constant $= 2.9 \times 10^{-3} m K$).

Find the emissive power from the $0.3 \, cm^2$ surface of a tungsten filament bulb at $3000 \, K$ temperature. Take emissivity $e = 0.4$ for the tungsten bulb. (in $, W$)

Star $A$ has radius $r$ and surface temperature $T$,while star $B$ has radius $4r$ and surface temperature $T/2$. The ratio of the power radiated by the two stars,$P_A : P_B$,is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module