The rectangular surface of area $8$ cm $ \times $ 4cm of a black body at a temperature of ${127^o}C$ emits energy at the rate of $E$ per second. If the length and breadth of the surface are each reduced to half of the initial value and the temperature is raised to ${327^o}C$, the rate of emission of energy will become
Medium
Download our app for free and get started
(d) ${(Q)_{Black\,body}} = A\sigma {T^4}t$
==> $\frac{Q}{t} \propto $$P = A\sigma {T^4}$
Breadth are halved so area becomes one fourth.
==> $\frac{{{P_1}}}{{{P_2}}} = \frac{{{A_1}}}{{{A_2}}} \times {\left( {\frac{{{T_1}}}{{{T_2}}}} \right)^4}$
==> $\frac{{{A_1}}}{{({A_1}/4)}} \times \left( {\frac{{273 + 327}}{{273 + 127}}} \right)$
==> ${P_2} = \frac{{81}}{{64}}E$
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
- 1Two spherical bodies $\mathrm{A}$ (radius $6 \mathrm{~cm}$ ) and $\mathrm{B}$ (radius $18 \mathrm{~cm}$ ) are at temperature $\mathrm{T}_1$ and $\mathrm{T}_2$, respectively. The maximum intensity in the emission spectrum of $\mathrm{A}$ is at $500 \mathrm{~nm}$ and in that of $\mathrm{B}$ is at $1500 \mathrm{~nm}$. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by $A$ to that of $B$ ?View Solution
- 2A solid cube and a solid sphere of the same material have equal surface area. Both are at the same temperature ${120^o}C$, thenView Solution
- 3A body cools from ${50.0^o}C$ to ${49.9^o}C$ in $5\;s$. How long will it take to cool from ${40.0^o}C$ to ${39.9^o}C$? Assume the temperature of surroundings to be ${30.0^o}C$ and Newton's law of cooling to be valid ....... $\sec$View Solution
- 4A body takes $4\, {min}$. to cool from $61^{\circ} {C}$ to $59^{\circ} {C}$. If the temperature of the surroundings is $30^{\circ} {C}$, the time taken by the body to cool from $51^{\circ} {C}$ to $49^{\circ} {C}$ is $....\,min$View Solution
- 5Calculate radiation power for sphere whose temperature is $227^{\circ} C$ and radius $2\, m$ and emissivity $0.8$ (in $W$)View Solution
- 6A cup of tea cools from $80\,^oC$ to $60\,^oC$ in one minute. The ambient temperature is $30\,^oC$. In cooling from $60\,^oC$ to $50\,^oC$, it will take ....... $\sec$View Solution
- 7A body takes $5$ minutes for cooling from ${50^o}C$ to ${40^o}C.$ Its temperature comes down to ${33.33^o}C$ in next $5$ minutes. Temperature of surroundings is ....... $^oC$View Solution
- 8View SolutionUnder steady state, the temperature of a body
- 9View SolutionIf the initial temperatures of metallic sphere and disc, of the same mass, radius and nature are equal, then the ratio of their rate of cooling in same environment will be
- 10If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature $\theta_0$, the graph between the temperature $T$ of the metal and time t will be closest toView Solution