Energy management has become a crucial field in increasing the efficiency of our everyday use of energy.
One of the most energy consuming activities is the boiling of water. In order to understand the energy
consumption, you need to have understanding on thermodynamics and electricity.
Solve the calculation below:
We use an electric immersion heater to heat 2,0 liters water having temperature of 20C to the boiling
point. Specific heat capacity of water is 4,19 kJ/(kg C). The power of the heater is 1,50 kW and efficiency
of heating is 80 %. How much time does the heating take?
To solve this calculation, we can follow these steps:
Step 1: Calculate the mass of water.
The specific heat capacity of water is given as 4.19 kJ/(kg . °C).
We have 2.0 liters of water, and 1 liter of water weighs approximately 1 kg.
Therefore, the mass of water in kg would be: 2.0 kg.
Step 2: Calculate the energy required to heat the water.
To heat the water from 20°C to its boiling point, the temperature difference would be 100°C (boiling point of water is 100°C - 20°C initial temperature = 80°C temperature difference).
The energy required can be calculated using the formula:
Energy = mass of water x specific heat capacity x temperature difference.
Energy = 2.0 kg x 4.19 kJ/(kg.°C) x 80°C
Step 3: Calculate the time taken to heat the water.
The power of the heater is given as 1.50 kW and its efficiency is 80%.
Efficiency is defined as the ratio of useful energy output to the energy input.
So, the useful energy output = efficiency x energy input.
Useful energy output = 0.80 x Energy
The time taken can be calculated using the formula:
time = useful energy output / power
time = (0.80 x Energy) / 1.50 kW
Step 4: Substitute the calculated values.
Substitute the values from step 2 into step 3 equation and calculate the time.
time = (0.80 x (2.0 kg x 4.19 kJ/(kg.°C) x 80°C)) / 1.50 kW
Now, you can solve this equation to find the time taken to heat the water.
To solve this calculation, we need to understand the principles of energy and power.
First, let's calculate the amount of heat energy required to heat the water from 20°C to its boiling point. We'll use the formula:
Q = mcΔT
Where:
Q is the heat energy (in joules),
m is the mass of water (in kilograms),
c is the specific heat capacity of water (in kJ/(kg·°C)),
and ΔT is the change in temperature (in °C).
To find the mass of water, we'll convert the volume of water from liters to kilograms. The density of water is approximately 1 kg/L. Therefore:
Mass (m) = Volume × Density
m = 2.0 L × 1 kg/L
m = 2.0 kg
Now, we can calculate the heat energy:
Q = mcΔT
Q = (2.0 kg) × (4.19 kJ/(kg·°C)) × (100°C - 20°C)
Q = 2.0 kg × 4.19 kJ/(kg·°C) × 80°C
Q = 671.2 kJ
Next, let's calculate the time it takes to heat the water using the power of the heater and its efficiency. Power is defined as the rate at which energy is transferred or converted, and it is measured in watts (W).
The formula for calculating the time (t) is:
t = Q / (P × efficiency)
Where:
t is the time (in seconds),
Q is the heat energy (in joules),
P is the power of the heater (in watts),
and efficiency is the efficiency of the heating process (expressed as a decimal).
Let's plug in the values into the equation:
t = 671.2 kJ / (1.50 kW × 0.80)
t = 671.2 kJ / 1.20 kW
t ≈ 559.33 seconds
Therefore, the heating process will take approximately 559.33 seconds or about 9 minutes and 19 seconds.