The Easy Bake Oven is a common toy for young children who want to emulate the process of cooking. Suppose this oven is plugged into a 120 V electrical outlet and "cooks" the food by using a 144 ohm resistor light bulb that converts electrical energy to both light and heat energy. If the light bulb converts 75% of the electrical energy to thermal energy, and the oven is used for a total of 15.0 hours during one month, to the nearest hundredth of a megajoule, how much thermal energy was produced?
Q=0.75V²t/R=
=0.75•120²•15•3600/144=4050000 J = 4.05 MJ
To find the amount of thermal energy produced by the Easy Bake Oven, we need to calculate the electrical energy consumed by the light bulb and then multiply it by the efficiency factor.
First, let's calculate the electrical energy consumed by the light bulb using the formula:
Electrical energy (in joules) = Power (in watts) × Time (in seconds)
The power can be calculated using Ohm's law, which states:
Power (in watts) = (Voltage (in volts))^2 / Resistance (in ohms)
Given that the voltage is 120 V and the resistance is 144 ohms, we can substitute these values into the formula:
Power (in watts) = (120 V)^2 / 144 ohms
Calculating this:
Power (in watts) = 100 V^2 / 144 ohms
= 10000 V^2 / 144 ohms
= 694.44 W (rounded to the nearest hundredth)
Now, let's calculate the electrical energy consumed during one month, which is 15.0 hours.
Time (in seconds) = 15.0 hours × 60 minutes/hour × 60 seconds/minute
= 15.0 × 60 × 60 seconds
= 54,000 seconds
Electrical energy (in joules) = Power (in watts) × Time (in seconds)
= 694.44 W × 54,000 seconds
Multiplying these values:
Electrical energy (in joules) = 37,499,760 joules
Since the light bulb converts 75% of the electrical energy to thermal energy, we can calculate the thermal energy produced:
Thermal energy (in joules) = Electrical energy (in joules) × Efficiency factor
= 37,499,760 joules × 0.75
Calculating this:
Thermal energy (in joules) = 28,124,820 joules
To convert this to megajoules, divide by 1,000,000:
Thermal energy (in megajoules) = 28,124,820 joules / 1,000,000
= 28.12 megajoules (rounded to the nearest hundredth)
Therefore, the amount of thermal energy produced by the Easy Bake Oven is approximately 28.12 megajoules.