Answer :

**Given:**Thickness of the container: x = 2 mm = 0.002 m

Thermal conductivity of the container: K= 0.50 W m

^{–1}°C

^{–1}.

Temperature of the water: T

_{1}= 1 °C

Temperature of the ice bath: T

_{2}= 0 °C

Surface are in contact with the water: 0.05 m

^{2}

Speed of the block: v = 10 cm/s = 0.1 m/s

g = 10 m/s

^{2}

**Formula used:**

Rate of amount of heat flowing or heat current is given as:

Here, Δθ is the amount of heat transferred, ΔT is the temperature difference, K is the thermal conductivity of the material, A is the area of cross section of the material and x is the thickness or length of the material.

The effect of the block going down and the heat transfer has one identity in common, which is power.

Power due to a block of mass M moving with constant velocity is given as

Here W is the work done by the block.

∴ P = (mg).v

∴ P = M× 10× 0.1

∴ P = M× 1

Also in terms of Heat Energy: P= Energy per unit time

Hence, the mass of the block is 12.5 kg.

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