$A$ perfectly black body emits radiation at a temperature $T_1 \ K$. If it is to radiate at $16$ times this power,its temperature $T_2 \ K$ should be: (in $T_1$)

The radiation emitted by a star $A$ is $10000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $6000 \ K$ and $2000 \ K$ respectively,the ratio of the radii of the star $A$ and the sun is: (in $: 1$)

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

$A$ 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.

The rate of radiation of a black body at $0^{\circ} C$ is $E \text{ J}s^{-1}$. The rate of radiation of the black body at $273^{\circ} C$ will be

$A$ solid copper sphere (density $\rho$ and specific heat capacity $c$) of radius $r$ at an initial temperature $200 \, K$ is suspended inside a chamber whose walls are at almost $0 \, K$. The time required (in $\mu s$) for the temperature of the sphere to drop to $100 \, K$ is: