JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Heat & Thermodynamics

Due to cold weather a 1 m water pipe of cross-sectional area

1 cm^{2}

is filled with ice at

- 1 0^{\circ} C

. Resistive heating is used to melt the ice. Current of 0.5 A is passed through

4 k Ω

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 \times 1 0^{5} J kg^{- 1}

, specific heat of ice

= 2 \times 1 0^{3} J kg^{- 1}

and density of ice

= 1 0^{3} kg / m^{3}

)

Answer: (C)

Solution

The ice mass is

m = ρ V = 1 0^{3} \times (1 \times 1 0^{- 4}) = 0.1 kg

. Warming it from

- 1 0^{\circ} C

0^{\circ} C

and then melting it needs

Q = m s Δ T + m L = 0.1 \times 2 \times 1 0^{3} \times 10 + 0.1 \times 3.33 \times 1 0^{5} = 3.53 \times 1 0^{4} J

. The resistor supplies

I^{2} R = (0.5)^{2} \times 4000 = 1000 W

, so the time is

t = \frac{3.53 \times 1 0 ^{4}}{1000} = 35.3 s

JEE Main · 2021 · 01 Sep 2021 · Shift 2 · Single correct option