How long would it take a 1.00 x 10^3 W heating element to melt 2.00kg of ice at -20 deg C, assuming all energy is absorbed by the ice?
3 second
To calculate the time it would take for a heating element to melt ice, we need to determine the amount of energy required to melt the ice and the rate at which the heating element transfers energy.
Step 1: Calculate energy required to melt the ice
The specific heat capacity of ice is approximately 2.09 J/g°C, meaning it takes 2.09 Joules of energy to raise the temperature of 1 gram of ice by 1 degree Celsius. Since the ice is at -20°C and we want to heat it up to 0°C (the melting point), we need to raise its temperature by 20 degrees Celsius.
Energy required = mass of ice x specific heat capacity x change in temperature
Energy required = 2000 grams x 2.09 J/g°C x 20°C
Step 2: Calculate the time taken by the heating element
The power rating of the heating element is given as 1.00 x 10^3 W (Watts), which represents the rate at which energy is transferred.
Time taken = Energy required / Power rating
Time taken = (2000 grams x 2.09 J/g°C x 20°C) / (1.00 x 10^3 W)
By plugging in the values and performing the calculation, we can determine the answer.