One end of an insulated metal rod is maintained at 100 ∘c and the other end is maintained at 0.00 ∘c by an ice–water mixture. the rod has a length of 70.0 cm and a cross-sectional area of 1.10 cm2 . the heat conducted by the rod melts a mass of 8.70 g of ice in a time of 15.0 min .
find the thermal conductivity k of the metal?
k= w/(m. k)

Explanation:

Given:

temperature at the hotter end,

temperature at the cooler end,

length of rod through which the heat travels,

cross-sectional area of rod,

mass of ice melted at zero degree Celsius,

time taken for the melting of ice,

thermal conductivity k=?

By Fourier's Law of conduction we have:

......................................(1)

where:

=rate of heat transfer

dT= temperature difference across the length dx

Now, we need the total heat transfer according to the condition:

we know the latent heat of fusion of ice,  

Now the heat rate:

Now using eq,(1)

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