Answer
$\dot{Q}_{air}=2.34\ kW$
Work Step by Step
The energy balance for a single ball:
$Q=\Delta U=mc(T_2-T_1)$
With the mass given by:
$m=\rho(\frac{\pi}{6} D³)$
Since $\rho=8085\ kg/m³, D=0.012\ m$
$m=0.007315\ kg$
Given $c=0.480\ kJ/kg.K, T_2=850°C, T_1=900°C$:
We get to: $Q_{ball}=-0.1756\ kJ$
For a frequency of $\dot{n}=800\ balls/min$
$\dot{Q}_{air}=-\dot{n}Q_{ball}$
Hence,
$\dot{Q}_{air}=140.5\ kJ/min=2.34\ kW$
