Given, the length of the water pipe, L = 1 m
The cross-sectional area of the water pipe, A
=1cm2=10−4m2 The temperature of the ice = -10ºC
Current passing in the conductor, I = 0.5 A
Resistance of the conductor, R = 4 kΩ
The latent heat of fusion for ice,
,Li=3.33×105J∕kg The density of the ice, d
=1000kg∕m3 The specific heat of the ice,
cp,ice=2×103J∕kg Heat required to melt the ice at 10°C to 0°C
Q=mcpΔT+mLi Q=dVcpΔT+dVLf =1000×10−4×2×103×(10)+1000×10−4×3.33×105
(∵V=A×L) = 35300 J
According to the Joule’s law of heating,
H=I2Rt ⇒
35300=(0.5)2(4000)(t) t = 35.3 s
Thus, the minimum time required to melt the ice is 35.3 s.