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A kettle with $2$ litre water at $27 ° C$ is heated by operating coil heater of power $1 k W$ . The heat is lost to the atmosphere at constant rate $160 J / s$ , when its lid is open. In how much time will water heated to $77 ° C$ with the lid open? (specific heat of water $= 4.2 k J / {}^{\circ}C \cdot k g$ )

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$6 \min 2 s$

$14 m i n$

$8 m i n 20 s_{}$

$7 m i n$

answer is A.

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Detailed Solution

Net power available per second,

$P = 1000 - 160 = 840 J / s$

Heat required,

$Q = m s Δ θ = (2) (4200) (77 - 27)$ $= 420000 J$

Therefore time required $= 8 m i n 20 s e c$

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