Question

Плиз помогите у меня кр по этой задаче?!!! В електричний чайник налили воду за температури 12°.Через 4 хв.після ввімкнення чайника вода закипіла.Визначте масу води,якщо ККД чайника-91 відсоток,сила струму в його нагрівальному елементі-10А,напруга в мережі-220В

Answer 1

Решение на фото внизу.

Answer 2

Problem Analysis

To solve this problem, we need to determine the mass of water in the electric kettle. We are given the initial temperature of the water, the time it takes for the water to boil, the efficiency of the kettle, and the current and voltage in its heating element.

Solution

To find the mass of water, we can use the formula:

Q = m * c * ΔT

Where: - Q is the heat energy absorbed by the water (in Joules) - m is the mass of water (in kilograms) - c is the specific heat capacity of water (approximately 4.18 J/g°C) - ΔT is the change in temperature (in °C)

We can calculate the heat energy absorbed by the water using the formula:

Q = P * t

Where: - P is the power of the kettle (in Watts) - t is the time taken for the water to boil (in seconds)

Since the power (P) is given by the product of current (I) and voltage (V):

P = I * V

We are given that the efficiency (η) of the kettle is 91%. The efficiency is defined as the ratio of the useful output energy to the input energy. In this case, the useful output energy is the heat energy absorbed by the water (Q), and the input energy is the electrical energy supplied to the kettle (E).

η = Q / E

Since the efficiency is given, we can rearrange the equation to solve for the electrical energy supplied to the kettle:

E = Q / η

Finally, we can substitute the value of Q from the previous equation and solve for the mass of water (m):

E = m * c * ΔT / η

Calculation

Let's calculate the mass of water using the given values:

- Initial temperature of the water (T1) = 12°C - Time taken for the water to boil (t) = 4 minutes = 240 seconds - Efficiency of the kettle (η) = 91% - Current in the heating element (I) = 10A - Voltage in the circuit (V) = 220V - Specific heat capacity of water (c) = 4.18 J/g°C

First, let's calculate the power of the kettle (P):

P = I * V = 10A * 220V = 2200W

Next, let's calculate the heat energy absorbed by the water (Q):

Q = P * t = 2200W * 240s = 528000J

Now, let's calculate the electrical energy supplied to the kettle (E):

E = Q / η = 528000J / 0.91 = 579120J

Finally, let's calculate the mass of water (m):

E = m * c * ΔT / η

579120J = m * 4.18 J/g°C * (100°C - 12°C) / 0.91

Simplifying the equation:

579120J = m * 4.18 J/g°C * 88°C / 0.91

m = 579120J / (4.18 J/g°C * 88°C / 0.91)

m ≈ 1500g

Therefore, the mass of water in the electric kettle is approximately 1500 grams.

Answer

The mass of water in the electric kettle is approximately 1500 grams.