A hot black body emits the energy at the rate of $16\ J\ m^{-2}\ s^{-1}$ and its most intense radiation corresponds to $20,000\ Å$ . When the temperature of this body is further increased and its most intense radiation corresponds to $10,000\ Å$ , then the energy radiated in $Jm^{-2}\ s^{-1}$ will be
Medium
Download our app for free and get started
Wein's displacement law is $:$
$\lambda_{\mathrm{m}} \cdot \mathrm{T}=\mathrm{b}$
i.e. $\mathrm{T} \propto \frac{1}{\lambda_{\mathrm{m}}}$
Here, $\lambda_{\mathrm{m}}$ becomes half.
$\therefore$ Temperature doubles.
Also $e$ $=\sigma \mathrm{T}^{4}$
$\Rightarrow \frac{\mathrm{e}_{1}}{\mathrm{e}_{2}}=\left(\frac{\mathrm{T}_{1}}{\mathrm{T}_{2}}\right)^{4}$
$\Rightarrow \mathrm{e}_{2}=\left(\frac{\mathrm{T}_{2}}{\mathrm{T}_{1}}\right)^{4} \cdot \mathrm{e}_{1}=(2)^{4} \cdot 16$
$=16.16=256 \mathrm{J} \mathrm{m}^{-2} \mathrm{s}^{-1}$
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
- 1View SolutionHalf part of ice block is covered with black cloth and rest half is covered with white cloth and then it is kept in sunlight. After some time clothes are removed to see the melted ice. Which of the following statements is correct
- 2If the radius of a star is $R$ and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is $Q$?View Solution
($\sigma$ stands for Stefan's constant)
- 3If a liquid takes $30 \;sec$ in cooling from $80^{\circ} C$ to $70^{\circ} C$ and $70 \;sec$ in cooling from $60^{\circ} C$ to $50^{\circ} C$, then find the room temperature.View Solution
- 4Two rods of same material have same length and area. The heat $\Delta Q$ flows through them for $12\,minutes$ when they are jointed in series. If now both the rods are joined in parallel, then the same amount of heat $\Delta Q$ will flow in ........ $\min$View Solution
- 5A particular star (assuming it as a black body) has a surface temperature of about $5 \times {10^4}K.$The wavelength in nanometers at which its radiation becomes maximum is $(b = 0.0029 mK)$View Solution
- 6The length of the two rods made up of the same metal and having the same area of cross-section are $0.6 m$ and $0.8 m$ respectively. The temperature between the ends of first rod is ${90^o}C$ and ${60^o}C$ and that for the other rod is $150^oC$ and ${110^o}C$. For which rod the rate of conduction will be greaterView Solution
- 7A container contains hot water at ${100^o}C$. If in time ${T_1}$ temperature falls to ${80^o}C$ and in time ${T_2}$ temperature falls to ${60^o}C$ from ${80^o}C$, thenView Solution
- 8View SolutionA thermos flask is polished well
- 9A cup of coffee cools from $90^{\circ} \mathrm{C}$ to $80^{\circ} \mathrm{C}$ in $\mathrm{t}$ minutes, when the room temperature is $20^{\circ} \mathrm{C}$. The time taken by a similar cup of coffee to cool from $80^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ at a room temperature same at $20^{\circ} \mathrm{C}$ is :View Solution
- 10A rod of length $L$ with sides fully insulated is of a material whose thermal conductivity varies with $\alpha$ temperature as $ K= \frac{\alpha }{T}$, where $\alpha$ is a constant. The ends of the rod are kept at temperature $T_1$ and $T_2$. The temperature $T$ at $x,$ where $x$ is the distance from the end whose temperature is $T_1$ isView Solution