A refrigilator converts 5kg of water at 40c into ice at 0c in 20 minutes.Then it’s power is.........

To determine the power of the refrigerator that converts 5 kg of water at 40°C into ice at 0°C in 20 minutes, we need to consider the energy required for this process and how power is defined in terms of energy and time.

Understanding the Energy Transfer

The process involves two main steps: cooling the water from 40°C to 0°C and then freezing it into ice at 0°C. We will calculate the energy required for each step.

Step 1: Cooling the Water

First, we need to calculate the energy required to cool the water from 40°C to 0°C. The specific heat capacity of water is approximately 4.18 kJ/kg°C. The formula to calculate the energy (Q) required for this cooling process is:

Q = m × c × ΔT

• m = mass of water = 5 kg
• c = specific heat capacity of water = 4.18 kJ/kg°C
• ΔT = change in temperature = 40°C - 0°C = 40°C

Substituting these values into the formula gives:

Q1 = 5 kg × 4.18 kJ/kg°C × 40°C = 834 kJ

Step 2: Freezing the Water

Next, we need to calculate the energy required to freeze the water at 0°C. The latent heat of fusion for water is about 334 kJ/kg. The energy required for this phase change is calculated using:

Q2 = m × L

• L = latent heat of fusion = 334 kJ/kg

Thus, the energy required to freeze 5 kg of water is:

Q2 = 5 kg × 334 kJ/kg = 1670 kJ

Total Energy Required

The total energy (Q_total) needed for the entire process is the sum of the energy for cooling and the energy for freezing:

Q_total = Q1 + Q2 = 834 kJ + 1670 kJ = 2504 kJ

Calculating Power

Power is defined as the rate at which energy is transferred or converted, and it can be calculated using the formula:

Power (P) = Energy (Q_total) / Time (t)

• Q_total = 2504 kJ = 2504000 J (since 1 kJ = 1000 J)
• t = 20 minutes = 20 × 60 seconds = 1200 seconds

Now, substituting these values into the power formula gives:

P = 2504000 J / 1200 s ≈ 2086.67 W

Final Result

The power of the refrigerator is approximately 2087 watts (or about 2.09 kW). This means that the refrigerator needs to operate at this power level to convert 5 kg of water at 40°C into ice at 0°C within 20 minutes.