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A kettle with 2 litre water at 27^@C is ...

A kettle with 2 litre water at `27^@C` is heated by operating coil heater of power 1 kW. 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 kJ//^@C.kg)`

A

8 min 20 sec

B

6 min 2sec

C

14 min

D

7 min

Text Solution

Verified by Experts

The correct Answer is:
A
By the law of conservation of energy, energy given by heater must be equal to the sum of energy gained by water and energy lost from the lid.
`Pt=msDeltatheta`+ energy lost
i.e. , `1000t=2xx(4.2xx10^3)xx50+160t`
or `840t=8.4xx10^3xx50` or t=500sec = 8 min 20 sec.
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