Question

1. a man is cooking dinner and needs to bring 4 quarts of water (3.80 kilograms) from 20 °c to its boiling point of 100 °c.

a. how much thermal energy is required to achieve this? use the specific heat of water on page 333.
b. boiling 4 quarts of water in an uncovered pot can take about fifteen minutes. by covering the pot, the time it takes to boil is reduced. why might this be the case?

Explanation:

Part a

Step1: Recall heat energy formula

The formula for thermal energy required to change temperature is $Q = mc\Delta T$, where $m$ is mass, $c$ is specific heat of water, and $\Delta T$ is temperature change.

Step2: Define known values

$m = 3.80\ \text{kg}$, $c = 4186\ \text{J/(kg·°C)}$ (standard specific heat of water), $\Delta T = 100^\circ\text{C} - 20^\circ\text{C} = 80^\circ\text{C}$

Step3: Substitute values into formula

$Q = 3.80\ \text{kg} \times 4186\ \text{J/(kg·°C)} \times 80^\circ\text{C}$

Step4: Calculate the result

$Q = 3.80 \times 4186 \times 80 = 1,270,688\ \text{J}$

Covering the pot traps the warm, moist air above the water. This reduces heat loss from evaporation (which carries away thermal energy) and creates a layer of trapped air that acts as insulation, keeping more heat focused on heating the water. Additionally, the trapped water vapor increases the pressure above the water slightly, which can raise the boiling point marginally, but the primary effect is reducing heat loss to the surroundings, so the water reaches boiling temperature faster.

Answer:

$1.27 \times 10^6\ \text{J}$ (or 1,270,688 J)

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Part b