A microwave rated at 1000 W heats a 500-g glass of water from 10°C to 55°C in 2.0 min. Determine the efficiency of the energy transformation
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To determine the efficiency of the energy transformation, we first need to calculate the amount of energy transferred to heat the water.
The formula to calculate the energy transferred is:
Energy Transferred = Power × Time
Given:
Power of the microwave = 1000 W
Time taken = 2.0 min = 2.0 × 60 seconds = 120 seconds
Now we can calculate the energy transferred:
Energy Transferred = 1000 W × 120 seconds = 120,000 Joules
Next, we need to calculate the energy required to heat the water using the specific heat capacity formula:
Energy Required = Mass × Specific Heat Capacity × Temperature Change
Given:
Mass of water = 500 g
Specific Heat Capacity of water = 4.18 J/g°C (approximately)
Initial Temperature = 10°C
Final Temperature = 55°C
Temperature Change = Final Temperature - Initial Temperature = 55°C - 10°C = 45°C
Energy Required = 500 g × 4.18 J/g°C × 45°C = 94,050 Joules (approximately)
Now that we have the energy transferred and the energy required, we can calculate the efficiency:
Efficiency = (Energy Transferred / Energy Required) × 100
Efficiency = (120,000 Joules / 94,050 Joules) × 100 ≈ 127.6%
Therefore, the efficiency of the energy transformation in heating the glass of water is approximately 127.6%.