How long does it take the sun to melt a block of ice?

[angelbluw15]

Homework Statement

How long does it take the Sun to melt a block of ice at 0°C with an area of 1.10 m2 and thickness 1.07 cm? Assume that the Sun's rays make an angle of 31.1° with the normal to the area, and that the emissivity of ice is 0.0400.

Homework Equations

Q/t = IeAcos(theta)

The Attempt at a Solution

ok, I've done multiple attempts and am still not getting the correct answer!

1) Q/t = IeAcos(Theta)
Q/t = (1000 W/m^2)(0.04)(1.10cos(31.1)) = 37.6 J/s
but from this number, I don't understand how to find time, should it be one??

or
A*h *ρ *L /t = IeACOSθ
t = time for ice to melt = IeCOSθ /h *ρ *L
t = (1000 W/m^2)(0.04)(cos(31.1)/(0.0107 m)(917 kg/m^3)(3.33*10^5 J/kg)
t= 1.05*10^-5 s

but, that doesn't work either. I've been trying this problem all afternoon, please help!

 

[haruspex]

A*h *ρ *L /t = IeACOSθ
t = time for ice to melt = IeCOSθ /h *ρ *L
t = (1000 W/m^2)(0.04)(cos(31.1)/(0.0107 m)(917 kg/m^3)(3.33*10^5 J/kg)

The OP has blundered in manipulating the equation, yielding, numerically, 1/t instead of t.