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)`

Options

A. 7 min
B. 6 min 2 s
C. 8 min 20 s
D. 14 min

Answer

C

Explanation

As shown in fig the net heat absorbed by the water to raise its temperature`=(1000-160)=840J//s` . Now, the heat required to raise the temperature of water from `27^(@)C` to `77^(@)C` is `Q=mcDeltaT=2xx4200xx50J` . Therefore the time required
`t=(Q)/(840)=(2xx4200xx50)/(840)500s`
`=8min20s`