Answer:
The time is 0.713 sec.
Explanation:
Given that,
Weight of water = 4 liters
Initial temperature = 128°C
Power = 1400 Watts
Final temperature = 708°C
Weight = 1.1 kg
Specific heat of steel = 0.46 kJ/kg°C
Specific heat of water = 4.18 kJ/kg°C
We need to calculate the heat gained by bucket
Using formula of heat
![Q_{b}=mc\Delta T](https://tex.z-dn.net/?f=Q_%7Bb%7D%3Dmc%5CDelta%20T)
Put the value into the formula
![Q_{b}=1.1\times0.46\times(70-12)](https://tex.z-dn.net/?f=Q_%7Bb%7D%3D1.1%5Ctimes0.46%5Ctimes%2870-12%29)
![Q_{b}=29.348\ kJ](https://tex.z-dn.net/?f=Q_%7Bb%7D%3D29.348%5C%20kJ)
We need to calculate the heat gained by water
Using formula of heat
![Q_{w}=mc\Delta T](https://tex.z-dn.net/?f=Q_%7Bw%7D%3Dmc%5CDelta%20T)
Put the value into the formula
![Q_{w}=4\times4.18\times(70-12)](https://tex.z-dn.net/?f=Q_%7Bw%7D%3D4%5Ctimes4.18%5Ctimes%2870-12%29)
![Q_{w}=969.76\ kJ](https://tex.z-dn.net/?f=Q_%7Bw%7D%3D969.76%5C%20kJ)
We need to calculate the total heat
Using formula of heat
![Q=Q_{b}+Q_{w}](https://tex.z-dn.net/?f=Q%3DQ_%7Bb%7D%2BQ_%7Bw%7D)
Put the value into the formula
![Q=29.348+969.76](https://tex.z-dn.net/?f=Q%3D29.348%2B969.76)
![Q=999.108\ kJ](https://tex.z-dn.net/?f=Q%3D999.108%5C%20kJ)
We need to calculate the time
Using formula of time
![t=\dfrac{Q}{P}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7BQ%7D%7BP%7D)
Put the value into the formula
![t=\dfrac{999.108}{1400}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B999.108%7D%7B1400%7D)
![t=0.713\ sec](https://tex.z-dn.net/?f=t%3D0.713%5C%20sec)
Hence, The time is 0.713 sec.