The emissive power of a sphere of area $0.04 \,m^2$ is $0.7 \,kcal \,s^{-1} \,m^{-2}$. The amount of heat radiated in $20 \,s$ is: (in $\,kcal$)

The wavelength of maximum emitted energy $(\lambda_m)$ of a body at $700 \ K$ is $4.08 \ \mu m$. If the temperature of the body is raised to $1400 \ K$,then the value of $\lambda_m$ will be (in $\mu m$)

$A$ black body radiates power $P$ and maximum energy is radiated by it at a wavelength $\lambda_0$. The temperature of the black body is now changed such that it radiates maximum energy at the wavelength $\frac{\lambda_0}{4}$. The power radiated by it at the new temperature is (in $P$)

The black body spectrum of an object $O_1$ is such that its radiant intensity (i.e.,intensity per unit wavelength interval) is maximum at a wavelength of $200\,nm$. Another object $O_2$ has the maximum radiant intensity at $600\,nm$. The ratio of power emitted per unit area by source $O_1$ to that of source $O_2$ is

$A$ black body has a maximum wavelength $\lambda_{m}$ at a temperature of $2000 \ K$. Its maximum wavelength at $3000 \ K$ will be:

The temperature of a black body is $2880 \, K$. $U_1$ is the energy of radiation between $499 \, nm$ and $500 \, nm$,$U_2$ is the energy of radiation between $999 \, nm$ and $1000 \, nm$,and $U_3$ is the energy of radiation between $1499 \, nm$ and $1500 \, nm$. Given Wien's constant $b = 2.88 \times 10^6 \, nm \cdot K$,which of the following is correct?