Question

Электрический чайник нагревает 2 л воды от 10 до 100 градусов за 7 минут. Какова длина никелиновой проволоки, из которой изготовлен нагревательный элемент? Площадь сечения проволоки равна 0,63 мм^2, КПД чайника 80%, напряжение в сети 220 В. удельная теплоемкость воды 4,2 кДж/(кг*К)

Answer 1

1 дано потом решение

Answer 2

Calculation of the Length of the Nichrome Wire

To calculate the length of the nichrome wire used in the heating element of the electric kettle, we can use the formula:

Q = m * c * ΔT

Where: - Q is the amount of heat transferred (in joules) - m is the mass of water (in kilograms) - c is the specific heat capacity of water (in joules per kilogram per degree Celsius) - ΔT is the change in temperature (in degrees Celsius)

In this case, we know that the kettle heats 2 liters (or 2 kilograms) of water from 10 to 100 degrees Celsius in 7 minutes. We also know that the specific heat capacity of water is 4.2 kJ/(kg*K).

Let's calculate the amount of heat transferred:

Q = m * c * ΔT = 2 kg * 4.2 kJ/(kg*K) * (100 - 10)°C = 2 * 4.2 * 90 kJ = 756 kJ

Now, let's calculate the power used by the kettle:

Power = Energy / Time

Since the kettle heats the water in 7 minutes, which is equal to 420 seconds, the power used can be calculated as:

Power = 756 kJ / 420 s = 1.8 kW

The power used by the kettle is 1.8 kW.

To calculate the length of the nichrome wire, we can use the formula:

Power = (Resistance * Current^2)

Since we know the power and the voltage (220 V), we can calculate the current:

Current = Power / Voltage = 1.8 kW / 220 V = 8.18 A

Now, let's calculate the resistance of the nichrome wire:

Resistance = Voltage / Current = 220 V / 8.18 A = 26.89 Ω

To calculate the length of the nichrome wire, we need to know the resistivity of the wire material. Unfortunately, the resistivity of nichrome wire is not provided in the question. Therefore, it is not possible to calculate the exact length of the wire without this information.

However, if we assume a resistivity value for nichrome wire (approximately 1.10 x 10^-6 Ω*m), we can use the formula:

Resistance = (Resistivity * Length) / Cross-Sectional Area

Given that the cross-sectional area of the wire is 0.63 mm^2 (or 0.63 x 10^-6 m^2), we can rearrange the formula to solve for the length:

Length = (Resistance * Cross-Sectional Area) / Resistivity = (26.89 Ω * 0.63 x 10^-6 m^2) / (1.10 x 10^-6 Ω*m)

Using this formula, we can calculate the length of the nichrome wire. However, please note that the exact value of the resistivity of the nichrome wire is required for an accurate calculation.

Conclusion

In conclusion, the length of the nichrome wire used in the heating element of the electric kettle cannot be determined without knowing the resistivity of the wire material.