Question

One end of metal bar 0.001 m² cross sectional area and 0.5 m length is in contact of steam and another end in contact of ice at 0°C. If the thermal conductivity is 0.2 cal /s cm°C, then mass of Ice melt per min is

Answer 1

The mass of ice melt per min is 3 gram

Explanation:

Given

Length of the metal bar l = 0.5 m

Cross-sectional area of the bar A = 0.001 m²

Change in temperature ΔT = 100 °C - 0 °C = 100 °C

Time t = 1 min = 60 seconds

Thermal conductivity of the metal rod K = 0.2 cal/s-cm°C = 20 cal/s-m°C

Latent heat of ice L = 80 cal/g

The heat required by ice Q = mL, where m is the mass of the ice melt

We also know that

$Q=\frac{KA\Delta T t}{l}$

Thus,

$mL=\frac{KA\Delta T t}{l}$

$\implies m=\frac{KA\Delta T t}{lL}$

$\implies m=\frac{20\times 0.001\times 100\times 60}{0.5\times 80}$

$\implies m=3$ g

Hope this answer is helpful.

Know More:

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