Radiation energy corresponding to the temperature $T$ of the sun is $E$. If its temperature is doubled, then its radiation energy will be: (1990)
According to Stefan's law, $E \propto T^4$. When temperature is doubled ($2T$), the energy becomes $E' \propto (2T)^4 = 16 T^4$. So, $E' = 16E$.
A black body is at a temperature of $500 \text{ K}$. It emits energy at a rate which is proportional to: (1997)
According to Stefan-Boltzmann law, the rate of emission of radiant energy by a black body is proportional to the fourth power of its absolute temperature, $E \propto T^4$. Here, $T = 500 \text{ K}$, so $E \propto (500)^4$.
If the temperature of the sun is doubled, the rate of energy received on earth will be increased by a factor of: (1998)
The rate of energy received on earth is directly proportional to the rate of energy radiated by the sun. By Stefan's law, $E \propto T^4$. If $T$ is doubled, $E' \propto (2T)^4 = 16 T^4 = 16E$.
The total radiant energy per unit area, normal to the direction of incidence, received at a distance $R$ from the center of a star of radius $r$, whose outer surface radiates as a black body at a temperature $T$ $K$ is given by: (2010 Pre)
(Where $\sigma$ is Stefan’s Constant)
Radiant energy per unit area per unit time (Intensity) at distance $R$ is $I = \frac{P}{4\pi R^2} = \frac{\sigma (4\pi r^2) T^4}{4\pi R^2} = \frac{\sigma r^2 T^4}{R^2}$.
A black body is at $727^{\circ}\text{C}$. It emits energy at a rate which is proportional to (2007)
According to Stefan's law, $E \propto T^4$. Here $T = 727 + 273 = 1000 \text{ K}$. Therefore, $E \propto (1000)^4$.
A block body at $1227^{\circ}\text{C}$ emits radiations with maximum intensity at a wavelength of $5000\text{ \AA}$. If the temperature of the body is increased by $1000^{\circ}\text{C}$, the maximum intensity will be observed at (2006)
From Wien's displacement law, $\lambda_m T = \text{constant}$. $\lambda_1 T_1 = \lambda_2 T_2 \Rightarrow 5000 \times (1227+273) = \lambda_2 \times (1227+1000+273) \Rightarrow \lambda_2 = \frac{5000 \times 1500}{2500} = 3000\text{ \AA}$.
We consider the radiation emitted by the human, body. Which of the following statements is true: (2003)
The temperature of the human body is about $310 \text{ K}$. According to Wien's law, the maximum emission wavelength is around $9.3 \mu\text{m}$, which falls in the infrared region.
The Wien’s displacement law express relation between (2002)
Wien's displacement law states that the wavelength $\lambda_m$ corresponding to maximum spectral emissive power of a black body is inversely proportional to its absolute temperature $T$. So, it relates $\lambda_m$ and $T$.
Which of the following is best close to an ideal black body: (2002)
Ferry's black body consists of a hollow double-walled sphere with a small opening. Radiation entering it suffers multiple reflections and gets absorbed. So a cavity maintained at constant temperature is the closest to an ideal black body.
For a black body at temperature $727^{\circ}\text{C}$, its radiating power is $60 \text{ watt}$ and temperature of surrounding is $227^{\circ}\text{C}$. If temperature of black body is changed to $1227^{\circ}\text{C}$ then its radiating power will be: (2002)
Radiating power $P = \sigma A (T^4 - T_0^4)$. $\frac{P_2}{P_1} = \frac{T_2^4 - T_0^4}{T_1^4 - T_0^4} = \frac{1500^4 - 500^4}{1000^4 - 500^4} = \frac{3^4 - 1^4}{2^4 - 1^4} = \frac{80}{15} = \frac{16}{3}$. $P_2 = \frac{16}{3} \times 60 = 320 \text{ W}$.