Question

A microwave oven is used to heat 250 g of water. On its maximum setting, the oven can raise the temperature of the liquid water from 20⁰C to 100⁰C in 1 min 45 s (= 105 s). If the power input from the oven to the water remains constant, determine how many grams of water will boil away if the oven is operated for 3 minutes (rather than just 1 minute 45 seconds)?

Answer 1

Let's calculate the answer step by step.

First, let's calculate the heat gained by the water. We can use the formula:

Heat gained = mass of water * specific heat capacity * temperature change

The temperature change is 100°C - 20°C = 80°C.

Now, let's calculate the mass of water that will boil away. We know that the oven can raise the temperature of 250 g of water from 20°C to 100°C in 105 seconds.

Using the formula:

Heat gained = mass of water * specific heat capacity * temperature change

We then rearrange the formula to solve for the mass of water:

mass of water = Heat gained / (specific heat capacity * temperature change)

Substituting the values:

mass of water = (Heat gained in 105 seconds) / (specific heat capacity * temperature change)

afterwhich you calculate the heat gained in 105 seconds:

Heat gained = mass of water * specific heat capacity * temperature change

Substituting the values:

Heat gained = 250 g * 4.18 J/g°C * 80°C

let's calculate the mass of water that will boil away if the oven is operated for 3 minutes (180 seconds):

mass of water boiled away = (Heat gained in 180 seconds) / (specific heat capacity * temperature change)

Substituting the values:

mass of water boiled away = (Heat gained in 105 seconds) / (specific heat capacity * temperature change) * 180 / 105

mass of water boiled away = (250 g * 4.18 J/g°C * 80°C) / (4.18 J/g°C * 80°C) * 180 / 105

mass of water boiled away = 250 g * (180 / 105)

mass of water boiled away ≈ 428.57 g

Therefore, approximately 428.57 grams of water will boil away if the oven is operated for 3 minutes.

Explanation:

To determine the number of grams of water that will boil away, we can use the equation:

Heat gained by water = Heat lost by water vaporized

We can calculate the heat gained by the water using the specific heat capacity formula:

Heat gained = mass of water * specific heat capacity * temperature change

Since the oven is operated for 3 minutes, we need to calculate the heat gained by the water for this duration. Let's calculate it step by step.