If a substance at temperature $T$ is kept in surroundings at temperature $T_S$,what is the net rate of loss of radiation energy?

$A$ sphere and a cube,both made of copper,have equal volumes and are black. They are allowed to cool at the same temperature and in the same atmosphere. The ratio of their rate of loss of heat 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 energy spectrum of a black body exhibits a maximum of wavelength $\lambda_0$. The temperature of the black body is now changed such that the energy is maximum at wavelength $\frac{3\lambda_0}{2}$. The ratio of power radiated by the black body will be

The radiant energy from the sun incident normally at the surface of the earth is $20 \, kcal/(m^2 \cdot min)$. What would have been the radiant energy incident normally on the earth,if the sun had a temperature twice of the present one? (in $kcal/(m^2 \cdot min)$)

The power radiated by a black body is $P$ and it radiates maximum energy at wavelength $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{4}\lambda_0$,the power radiated by it becomes $nP$. The value of $n$ is