A microwave rated at 1000 W heats a 500 g glass of water from 10 degrees C to 55 degrees C in 2 minutes. Determine the efficiency of the energy transformation.
To determine the efficiency of the energy transformation, we need to compare the amount of energy that is used to heat the water to the amount of energy supplied by the microwave.
First, let's calculate the energy used to heat the water. We can use the formula:
Energy = mass * specific heat capacity * temperature change
Given:
Mass of water (m) = 500 g
Specific heat capacity of water (c) = 4.18 J/g°C (approximate value)
Temperature change (ΔT) = (55°C - 10°C) = 45°C
Energy used = 500 g * 4.18 J/g°C * 45°C = 93750 J
The next step is to calculate the energy supplied by the microwave. The power rating of the microwave is given as 1000 W, and the time taken to heat the water is 2 minutes. We need to convert the time to seconds since the power is given in watts (per second).
Time (t) = 2 minutes = 2 * 60 seconds = 120 seconds
Energy supplied = Power * Time = 1000 W * 120 s = 120000 J
Now, we have both the energy used to heat the water (93750 J) and the energy supplied by the microwave (120000 J). To calculate the efficiency, we use the formula:
Efficiency = (Energy used / Energy supplied) * 100
Efficiency = (93750 J / 120000 J) * 100 ≈ 78.12%
Therefore, the efficiency of the energy transformation from the microwave to heat the water is approximately 78.12%.