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. 8 min 20 sec
B. 6 min 2 sec
C. 14 min
D. 7 min

Answer

A

Explanation

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=ms Delta theta+` energy lost
`1000t=2xx4.2xx10^(3)xx50+160t`
`840t=8.4xx10^(3)xx50=500 sec=8 min 20 sec`