Question

Кипятильник, КПД которого равен 80%, изготовлен из нихромовой проволоки площадью поперечного сечения 0,84 мм2 и включен в сеть с напряжением 220 В. За 20мин с его помощью была нагрета вода объемом 4л от температуры 10оС до 90оС. Какова длина проволоки, из которой изготовлен проводник?

Answer 1

1) Нагреваем воду:
Q=c*m*(t₂-t1) = 4200*4*(90-10) = 1 344 000 Дж
2) Сопротивление провода:
R=ρ*L/S = 1,1*L/0,84 =1,3*L Ом
3) Мощность кипятильника:
N = U²/R = 220²/(1,3*L) ≈ 37230 /L

4) КПД:

КПД =Q/ (N*t)
0,80 = 1 344 000*L/ (37230*20*60)
0,80 = 0,03*L
L=0,80/0,03 ≈  27 м

Answer 2

Calculation of the Length of the Wire

To calculate the length of the wire used in the immersion heater, we can use the formula for power:

Power (P) = Voltage (V) x Current (I)

The power of the immersion heater can be calculated using the efficiency (η) and the formula:

Power (P) = Efficiency (η) x Input Power

Given that the efficiency (η) is 80% and the input power is the product of voltage (V) and current (I), we can rewrite the formula as:

Power (P) = 0.8 x (Voltage (V) x Current (I))

We know that the voltage (V) is 220 V, so we can substitute this value into the formula:

Power (P) = 0.8 x (220 V x Current (I))

To find the current (I), we can use the formula for power:

Power (P) = Current (I) x Resistance (R)

The resistance (R) can be calculated using the formula:

Resistance (R) = Resistivity (ρ) x Length (L) / Cross-sectional Area (A)

Given that the resistivity (ρ) of the wire is not provided, we cannot directly calculate the length of the wire. The resistivity depends on the material of the wire, which in this case is nichrome. However, the resistivity of nichrome wire is not provided in the question.

Therefore, without the resistivity of the wire, we cannot determine the length of the wire used in the immersion heater.

Please provide the resistivity of the nichrome wire so that we can calculate the length of the wire accurately.