Compare the rate of loss of heat from a metal sphere at $627^{\circ} C$ with the rate of loss of heat from the same sphere at $327^{\circ} C$,if the temperature of the surrounding is $27^{\circ} C$. (nearly)

Write the value and dimensional formula of the Stefan-Boltzmann constant.

$A$ black body at a temperature of $127^{\circ}C$ radiates heat at the rate of $1 \ cal/cm^2 \cdot s$. At a temperature of $527^{\circ}C$,the rate of heat radiation from the body in $cal/cm^2 \cdot s$ will be:

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 $= 2.9 \times 10^{-3} m K$).

$A$ planet of radius $R_{p}$ is revolving around a star of radius $R^{*}$ which is at temperature $T^{*}$. The distance between the star and the planet is $d$. If the planet's temperature is $f T^{*}$, then $f$ is proportional to

$A$ human body has a surface area of approximately $1 \,m^2$. The normal body temperature is $10 \,K$ above the surrounding room temperature $T_0$. Take the room temperature to be $T_0=300 \,K$. For $T_0=300 \,K$, and the value of $\sigma T_0^4=460 \,W/m^2$ (where $\sigma$ is the Stefan-Boltzmann constant). Which of the following option(s) is/are correct?
[$A$] The amount of energy radiated by the body in $1 \,s$ is close to $60 \,J$.
[$B$] If the surrounding temperature reduces by a small amount $\Delta T_0 < < T_0$, then to maintain the same body temperature the same (living) human being needs to radiate $\Delta W = 4 \sigma T_0^3 \Delta T_0$ more energy per unit time.
[$C$] Reducing the exposed surface area of the body (e.g., by curling up) allows humans to maintain the same body temperature while reducing the energy lost by radiation.
[$D$] If the body temperature rises significantly, then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths.