A solid at temperature $T_1$, is kept in an evacuated chamber at temperature $T_2>T_1$. The rate of increase of temperature of the body is proportional to:
1. $T_2-T_1$
2. $T^2_2 -T^2_1$
3. $T^3_2 -T^3_1$ 
4. $T^4_2 -T^4_1$

A black body at $227^{\circ}~\mathrm{C}$ radiates heat at the rate of $7~ \mathrm{cal-cm^{-2}s^{-1}}$.  At a temperature of $727^{\circ}~\mathrm{C}$, the rate of heat radiated in the same units will be:
1. $60$
2. $50$
3. $112$
4. $80$