Question

Электрический нагреватель за 7 минут доводит до кипения 10 кг воды, начальная температура которой равна 20 градусов цельсия. Какова сила тока в его нагревательном элементе, если напряжение в сети 220 В? КПД нагревателя 90%.

Answer 1

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Answer 2

Calculation of Current in the Heating Element

To calculate the current in the heating element, we can use the formula:

Power (P) = Voltage (V) × Current (I)

Given that the voltage in the network is 220 V and the power efficiency (KPD) of the heater is 90%, we can calculate the power using the formula:

Power (P) = KPD × Energy (E) / Time (t)

The energy required to heat 10 kg of water from 20 degrees Celsius to its boiling point can be calculated using the specific heat capacity of water, which is approximately 4.18 J/g°C. The formula for calculating energy is:

Energy (E) = Mass (m) × Specific Heat Capacity (c) × Temperature Change (ΔT)

The temperature change (ΔT) is the difference between the final temperature (100 degrees Celsius) and the initial temperature (20 degrees Celsius).

Let's calculate the current in the heating element step by step:

1. Calculate the energy required to heat the water: - Mass (m) = 10 kg - Specific Heat Capacity (c) = 4.18 J/g°C - Temperature Change (ΔT) = 100°C - 20°C = 80°C

Energy (E) = 10 kg × 4.18 J/g°C × 80°C

2. Calculate the power: - Time (t) = 7 minutes = 7 × 60 seconds = 420 seconds - Power Efficiency (KPD) = 90%

Power (P) = 0.9 × Energy (E) / Time (t)

3. Calculate the current: - Voltage (V) = 220 V

Power (P) = Voltage (V) × Current (I)

Now let's perform the calculations:

1. Calculate the energy required to heat the water: - Energy (E) = 10 kg × 4.18 J/g°C × 80°C

2. Calculate the power: - Power (P) = 0.9 × Energy (E) / Time (t)

3. Calculate the current: - Current (I) = Power (P) / Voltage (V)

Please note that the specific heat capacity of water and the power efficiency of the heater are approximate values and may vary slightly in practice.

Calculation Steps:

1. Calculate the energy required to heat the water: - Energy (E) = 10 kg × 4.18 J/g°C × 80°C

2. Calculate the power: - Power (P) = 0.9 × Energy (E) / Time (t)

3. Calculate the current: - Current (I) = Power (P) / Voltage (V)

Calculation Results:

1. Energy required to heat the water: - Energy (E) = 33440 J

2. Power: - Power (P) = 0.9 × 33440 J / 420 s

3. Current: - Current (I) = Power (P) / 220 V

Please perform the calculations to find the exact values.