Question

question 7 (1 point)
a 5000-w heater is used to heat water. how long will it take to heat 20 kg of water from 20°c to 100°c?
2 minutes
12 minutes
22 minutes
32 minutes

Explanation:

Step1: Recall the formula for heat energy

The heat energy \( Q \) required to raise the temperature of a substance is given by \( Q = mc\Delta T \), where \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature. For water, \( c = 4200 \, \text{J/(kg·°C)} \).

Step2: Calculate the change in temperature

\( \Delta T = 100 - 20 = 80 \, \text{°C} \)

Step3: Calculate the heat energy required

\( Q = mc\Delta T = 20 \, \text{kg} \times 4200 \, \text{J/(kg·°C)} \times 80 \, \text{°C} = 20 \times 4200 \times 80 \, \text{J} = 6720000 \, \text{J} \)

Step4: Recall the power formula

Power \( P = \frac{W}{t} \), where \( W \) is work (or energy) and \( t \) is time. Here, \( P = 5000 \, \text{W} \) and \( W = Q \). So, \( t = \frac{W}{P} \)

Step5: Calculate the time

\( t = \frac{6720000 \, \text{J}}{5000 \, \text{W}} = 1344 \, \text{seconds} \)

Step6: Convert seconds to minutes

\( t = \frac{1344}{60} \approx 22.4 \, \text{minutes} \), which is approximately 22 minutes.

Answer:

22 minutes (corresponding to the option: 22 minutes)