Question

Подошва стального утюга массой 700 г в процессе работы нагрелась от 20 до 200ºС. Сколько времени понадобилось для нагревания утюга, если его мощность равна 750 Вт, а КПД составляет 80%?

Answer 1

Η = $\frac{A poleznaja}{A zatrachennaja}$ * 100 %  ---------> η = $\frac{c * m * зt}{P * t}$ -------------> t = $\frac{c * m * зt}{P * n}$

c - удельная теплоёмкость ( для стали 460 Дж / кг * С )
m - масса ( 700 г = 0,7 кг )
Δt - разности температур ( 200 С - 20 С = 180 С )
P - мощность ( 750 Вт )
η - КПД = 80 % = 0,8 

t = $\fra460 * 0,7 * 180}{750 * 0,8}$ = $\frac{57960}{600}$ = 96.6 c = 1,61 мин 

Проверка:

η = $\frac{c * m * зt}{P * t }$ = $\frac{57960}{750 * 96.6}$ = $\frac{57960}{72450}$ = 0,8 * 100 = 80 % 

Answer 2

Calculation of Iron Heating Time

To calculate the time required for the iron to heat up from 20ºC to 200ºC, we can use the formula:

Q = m * c * ΔT

Where: - Q = heat energy required (in joules) - m = mass of the iron (in kg) - c = specific heat capacity of steel (in J/kgºC) - ΔT = change in temperature (in ºC)

The specific heat capacity of steel is approximately 490 J/kgºC.

The heat energy required can be calculated using the formula:

Q = P * t

Where: - P = power (in watts) - t = time (in seconds)

Given: - Mass of the iron, m = 0.7 kg (700 g) - Change in temperature, ΔT = 200ºC - 20ºC = 180ºC - Power, P = 750 W - Efficiency, η = 80% = 0.80

Let's calculate the time required for the iron to heat up.

Calculation Steps

1. Calculate the heat energy required to heat the iron from 20ºC to 200ºC. 2. Use the power and efficiency to find the time required for heating.

Step 1: Calculate Heat Energy Required

Using the formula Q = m * c * ΔT: Q = 0.7 kg * 490 J/kgºC * 180ºC

Step 2: Calculate Time Required

Using the formula Q = P * t and considering the efficiency: Q = P * η * t

Solving for t: t = Q / (P * η)

Let's calculate the time required using the given values.

Calculation

Q = 0.7 kg * 490 J/kgºC * 180ºC Q = 63,252 J

t = 63,252 J / (750 W * 0.80) t ≈ 83.94 seconds

So, it would take approximately 83.94 seconds for the iron to heat up from 20ºC to 200ºC.