Question

Электрический кипятильник с КПД 80% изготовлен из нихромовой проволоки сечением 0,84 мм2 и включен в сеть с напряжением 220 В.За 20 минут с его помощью было нагрето 4 л воды от 10°C до 90°C.Какова длина проволоки,из которой изготовлен кипятильник?Ответ укажите у метрах.

Answer 1

Длина =(КПД*U^2*время)/(c*m*плотность нихрома*удельное сопротивление нихрома*температуру) и всё это под корнем
l=√0.8*220^2*1200/4200*1000*110*10^-2*80=0.2 м

Answer 2

Calculation of the Length of the Wire

To calculate the length of the wire used to make the electric kettle, we need to consider the power efficiency (KPD) and the amount of water heated.

Given: - Power efficiency (KPD) = 80% - Cross-sectional area of the wire (S) = 0.84 mm² - Voltage (U) = 220 V - Time taken to heat the water (t) = 20 minutes - Amount of water heated (Q) = 4 liters - Initial temperature of the water (T1) = 10°C - Final temperature of the water (T2) = 90°C

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

P = (U^2 * S) / R

Where: - P is the power in watts - U is the voltage in volts - S is the cross-sectional area of the wire in square meters - R is the resistance of the wire in ohms

We can rearrange the formula to solve for R:

R = (U^2 * S) / P

The power (P) can be calculated using the formula:

P = Q * c * (T2 - T1) / t

Where: - Q is the amount of water in liters - c is the specific heat capacity of water (approximately 4.18 J/g°C) - T2 is the final temperature of the water in °C - T1 is the initial temperature of the water in °C - t is the time taken to heat the water in minutes

Let's calculate the length of the wire step by step.

1. Calculate the power (P) using the given values: - Q = 4 liters - c = 4.18 J/g°C - T2 = 90°C - T1 = 10°C - t = 20 minutes

P = (4 * 4.18 * (90 - 10)) / 20 = 83.6 watts 2. Calculate the resistance (R) using the formula: - U = 220 V - S = 0.84 mm² = 0.84 * 10^(-6) m²

R = (220^2 * 0.84 * 10^(-6)) / 83.6 = 2.21 ohms 3. Now, we can calculate the length of the wire (L) using the formula: - R = 2.21 ohms

L = R * (S / π) = 2.21 * (0.84 * 10^(-6) / π) ≈ 7.03 meters

Therefore, the length of the wire used to make the electric kettle is approximately 7.03 meters.

Please note that the calculations provided are based on the given information and assumptions.