To solve the problem it is necessary to apply the concepts related to heat flow,
The heat flux can be defined as
[tex]\frac{dQ}{dt} = H = \frac{kA\Delta T}{d}[/tex]
Where,
k = Thermal conductivity
A = Area of cross-sectional area
d = Length of the rod
[tex]\Delta T=[/tex] Temperature difference between the ends of the rod
[tex]k =388 W/m.\°C[/tex] Thermal conductivity of copper rod
[tex]A = 3.6 *10^{-4} m[/tex] Area of cross section of rod
[tex]\Delta T=100-0=100\°C[/tex] Temperature difference
[tex]d=1.3m[/tex] length of rod
Replacing then,
[tex]H = \frac{kA\Delta T}{d}[/tex]
[tex]H = \frac{(388)(3.6 *10^{-4})(100)}{1.3}[/tex]
[tex]H=10.7446J[/tex]
From the definition of heat flow we know that this is also equivalent
[tex]H = \dot{m}*L[/tex]
Where,
[tex]\dot{m} =[/tex] Mass per second
[tex]L = 334J/g[/tex] Latent heat of fusion of ice
Re-arrange to find [tex]\dot{m},[/tex]
[tex]H = \dot{m}*L[/tex]
[tex]\dot{m}=\frac{L}{H}[/tex]
[tex]\dot{m}=\frac{334}{10.7446}[/tex]
[tex]\dot{m} = 31.08g/s[/tex]
[tex]\dot{m}= 0.032g/s[/tex]
Therefore the mass of ice per second that melts is 0.032g
