Answer
$L=1.1m$
Work Step by Step
We can find the thickness of the ice layer as follows:
The heat flow rate for ice and water is given as
$\frac{Q_{ice}}{t}=K_{ice}A(\frac{T_1-T}{L})$........eq(1)
$\frac{Q_{w}}{t}=K_{w}A(\frac{T_2-T}{1.4m-L})$.......eq(2)
equating eq(1) and eq(2), we obtain:
$K_{ice}A(\frac{T_1-T}{L})=K_{w}A(\frac{T_2-T}{1.4m-L})$
This simplifies to:
$L=\frac{1.4m}{1+\frac{K_w(T_2-T_1)}{K_{ice}(T_2-T)}}$
We plug in the known values to obtain:
$L=\frac{1.4m}{1+\frac{(0.60W/m)(4.0C^{\circ}-0.0C^{\circ})}{(1.6W/m.K)(0.0C^{\circ}-(-5.4C^{\circ}))}}$
$L=1.1m$
