The unit of Stefan's constant $\sigma$ is

When the temperature of a black body is increased, the value of $\lambda_m$ changes from $0.26 \mu m$ to $0.13 \mu m$. What is the ratio of its emissive power corresponding to these temperatures?

The rate of radiation by a black body is $R$ at temperature $T$. Another body has the same area but an emissivity of $0.2$ and a temperature of $3T$. Its rate of radiation is: (in $R$)

$A$ 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.

Two spheres of the same material have radii $1 \ m$ and $4 \ m$ and temperatures $4000 \ K$ and $2000 \ K$ respectively. The energy radiated per second by the first sphere is

$A$ black metal foil is warmed by radiation from a small sphere at temperature $T$ and at a distance $d$. It is found that the power received by the foil is $P$. If both the temperature and distance are doubled,the power received by the foil will be: