\( - \frac{{dT}}{{dt}} = \frac{{e\sigma A}}{{ms}}\left( {{T^4} - T_0^4} \right)\,\,;\,\, - \frac{{dT}}{{dt}} = \frac{{4e\sigma AT_0^3}}{{ms}}\left( {\Delta T} \right)\)

\(T = {T_0} + \left( {{T_i} - {T_0}} \right){e^{ - kt}}\)

\(where\,k = \frac{{4e\sigma AT_0^3}}{{ms}}\)

\(k = \frac{{4e\sigma AT_0^3}}{{\rho vs}}\,\,;\,\,\left| {\frac{{dT}}{{dt}}} \right| \propto k\)

\(\therefore \left| {\frac{{dT}}{{dt}}} \right| \propto \frac{1}{{\rho s}}\)

\(\rho A{S_A} = 2000 \times 8 \times {10^2} = 16 \times {10^5}\)

\({\rho _B}{S_B} = 4000 \times {10^3} = 4 \times {10^6}\)

\({\rho _A}{S_A} < {\rho _B}{S_B}\)

\({\left| {\frac{{dT}}{{dt}}} \right|_A} > {\left| {\frac{{dT}}{{dt}}} \right|_B}\)