Due to cold weather a 1 m water pipe of cross-sectional area `1 cm^2` is filled with ice at ` - 10^@C`. Resistive heating is used to melt the ice. Current of 0.5 A is passed through `4 kOmega` resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ?
(Given latent heat of fusion for water/ice ` = 3.33 xx 10^5 J kg^(-1)`,
specific heat of ice ` = 2 xx 10^3 J kg^(-1)` and
density of ice `=10^3kg//m^3`)

Options

A. 3.53 s
B. 0.353 s
C. 35.3 s
D. 70.6 s

Answer

C

Explanation

`msDeltat + mL = I^(2)Rt`………. (i)
`therefore m = rhoV = 10^(3) xx 1 xx 10^(-4) = 0.1 kg`
`therefore` from eq.(i)
`rArr 0.1 xx [2 xx 10^(3) xx 10 + 3.33 xx 10^(5)] = 0.5^(2) xx 4 xx 10^(3) xx t`
`rArr t = 35.3 s`