One end of a 2.35 m long and 2.0 cm radius aluminum rod (K = 235 W m–1 K–1) is held at 20°C. The other end of the rod is in contact with a block of ice at its melting point. The rate (in kg s–1) at which ice melts is (Take latent heat of fusion for ice as × 105 J.kg

Engineering

Physics

Conduction of Heat

Question

One end of a 2.35 m long and 2.0 cm radius aluminum rod (K = 235 W m^–1 K^–1) is held at 20°C. The other end of the rod is in contact with a block of ice at its melting point. The rate (in kg s^–1) at which ice melts is (Take latent heat of fusion for ice as $\frac{10}{3}$ × 10⁵ J.kg^–1)

24π × 10^–6

4.8π × 10^–6

2.4π × 10^–6

48π × 10^–6

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$\frac{kA}{ℓ} (T_{2} - T_{1}) = \frac{dm}{dt} L$

$\frac{dm}{dt} = \frac{kA}{ℓL} (T_{2} - T_{1})$

$= \frac{100 \times π \times {(\frac{2}{100})}^{2}}{235 \times \frac{10}{3} \times 10^{5}} \times 20$

24π × 10^–7 kg/s