One end of an insulated metal rod is maintained at 100c and the other end is maintained at 0.00 c by an ice–water mixture. The rod has a length of 75.0cm and a cross-sectional area of 1.25cm . The heat conducted by the rod melts a mass of 6.15g of ice in a time of 10.0 min .find the thermal conductivity k of the metal?k= W/(m. K)

The thermal conductivity of the insulated metal rod is .

Explanation:

This is a situation of one-dimensional thermal conduction of a metal rod in a temperature gradient. The heat transfer rate through the metal rod is calculated by this expression:

Where:

- Heat transfer due to conduction, measured in watts.

- Length of the metal rod, measured in meters.

- Cross section area of the metal rod, measured in meters.

- Thermal conductivity, measured in .

Let assume that heat conducted to melt some ice was transfered at constant rate, so that definition of power can be translated as:

Where Q is the latent heat required to melt the ice, whose formula is:

Where:

- Mass of ice, measured in kilograms.

- Latent heat of fussion, measured in joules per gram.

The latent heat of fussion of water is equal to . Hence, the total heat received by the ice is:

Now, the heat transfer rate is:

Turning to the thermal conduction equation, thermal conductivity is cleared and computed after replacing remaining variables: (, , , )

The thermal conductivity of the insulated metal rod is .

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conduction, convection, radiation