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. \(80\)