High School

A microwave can reheat 1 cup of coffee in 30 seconds. It takes a coffee-maker 10 minutes to brew 12 cups of coffee. If the coffee-maker requires 900 watts of power and the microwave requires 1200 watts of power, does it require more energy to brew 12 cups with the coffee-maker or to reheat 12 cups of coffee in a microwave?

Answer :

The coffee maker is observed to require more energy than the microwave from the below calculations.

For microwave, the power required by microwave to reheat 1 cup = 1,200 watts

Time taken by microwave = 30 sec

Energy required for 12 cups of coffee = 12 × 36,000 joules = 432,000 Joules

For coffee-maker, the power required by coffee-maker to brew 12 cups of coffee = 900 watts

Coffee-maker's time = 10 minutes = 600 seconds.

Energy required by coffee-maker 540,000 Joules.

Thus, we can see that energy to brew 12 cup of coffee will require more amount of energy in comparison to amount of energy required by microwave to reheat 12 cups of coffee.

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Final answer:

To brew 12 cups of coffee with a coffee maker requires more energy compared to reheating 12 cups of coffee in a microwave.

Explanation:

To determine whether it requires more energy to brew 12 cups of coffee with a coffee maker or reheat 12 cups of coffee in a microwave, we need to calculate the energy used by each appliance.

The energy used by the coffee-maker can be calculated using the formula:

  1. Coffee-maker power: 900 watts
  2. Coffee-making time: 10 minutes (600 seconds)

Energy used by coffee-maker = Coffee-maker power x Coffee-making time = 900 watts x 600 seconds = 540,000 joules.

The energy used by the microwave can be calculated using the formula:

  1. Microwave power: 1200 watts
  2. Microwaving time for 1 cup: 30 seconds

Energy used by microwave for 1 cup = Microwave power x Microwaving time for 1 cup = 1200 watts x 30 seconds = 36,000 joules.

Energy used by microwave for 12 cups = Energy used by microwave for 1 cup x 12 = 36,000 joules x 12 = 432,000 joules.

Comparing the energy used, the coffee maker requires more energy to brew 12 cups of coffee, as it consumes 540,000 joules compared to the microwave's 432,000 joules. Therefore, it requires more energy to brew 12 cups with the coffee maker.