Answer
$\Delta t=71.90s$
Work Step by Step
The mass of the plate is given by:
$m=\rho V=\rho Ae$
With $\rho=2770\ kg/m³,\ A=0.03\ m²,\ e=0.005\ m$:
We get to $m=0.4155\ kg$
The energy balance for the plate:
$Q=\Delta U \rightarrow \dot{Q}\Delta t=mc(T_2-T_1)$
Since 90% of the iron's heat goes to the plate:
$\dot{Q}_{plate}=-0.9\dot{Q}_{iron}$
With $\dot{Q}_{iron}=-1000\ W,\ c=875\ kJ/kg.K,T_2=200°C, T_1=22°C$
$\dot{Q}_{plate}=900W$
Solving for the time interval: $\Delta t=71.90s$
