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Specific Heat Capacity

A kettle with...

Question

A kettle with $2 L$ water at $27^{\circ} C$ is heated by operating coil heater power $1 k W$ $. T h e h e a t i s l o s t t o t h e a t m o s p h e r e a t c o n s t a n t r a t e$ 160\ J/s $, w h e n i t s l i d i s o p e n . I n h o w m u c h t i m e w i l l w a t e r h e a t e d t o$ 77^{\circ}C $w i t h t h e l i d o p e n ? (s p e c i f i c h e a t o f w a t e r =$ 4.2 \ kJ/^{\circ} C - kg$)

8 m i n 20 s

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6 m i n 2 s e c

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14 m i n

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7 m i n

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Solution

The correct option is B $8 m i n 20 s$
$2 L$ water $= 2 k g$ .
$Δ T = 77 - 27 = 50$
heat absorbed by water
$Q = 2 \times 4200 \times 50 = 420000 J$
Heater is losing $160 J / s$ to atmosphere, so
Net Power, $P = 1000 - 160 = 840 W$
time, $t = \frac{Q}{P} = 500 s e c = 8 m i n 20 s e c$

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