an electric cattle is rated 5 kilowatt. how much time will it take to boil 15 kg of water initially at 15 degree celsius if it is connected to 230 volt supply.
To calculate the time it will take to boil the water, we need to use the power rating of the electric cattle, the amount of water, and the supply voltage.
First, let's convert the power rating from kilowatts (kW) to watts (W). Since 1 kilowatt is equal to 1000 watts, the power rating of 5 kilowatts can be converted to 5000 watts.
Next, we need to determine the amount of heat energy required to boil the water. This can be calculated using the formula:
Energy = mass × specific heat capacity × temperature change
The specific heat capacity of water is approximately 4.18 J/g°C (joules per gram per degree Celsius).
Given:
Mass of water (m) = 15 kg
Temperature change (ΔT) = boiling point of water (100°C) - initial temperature (15°C) = 85°C
Now, let's calculate the energy required:
Energy = 15 kg × 4.18 J/g°C × 85°C
To convert the mass from kg to grams, multiply by 1000:
Energy = (15 kg × 1000 g/kg) × 4.18 J/g°C × 85°C
Next, convert the energy from joules to watt-hours (Wh). Since 1 watt-hour is equal to 3600 joules, divide the energy by 3600:
Energy in watt-hours = [(15 kg × 1000 g/kg) × 4.18 J/g°C × 85°C] / 3600
Finally, calculate the time using the power rating and the energy consumed:
Time (in hours) = Energy in watt-hours / Power rating in watts
Time (in hours) = [(15 kg × 1000 g/kg) × 4.18 J/g°C × 85°C] / (5000 watts)
Now you can substitute the values and calculate the time required to boil the water.