Question

Воду массой 2 кг имеющую начальную температуру 25 градусов нагрели в электрическом чайнике до кипения 100 градусов за 6 мин. Найти КПД чайника. Мощность электрического чайника 2кВт. Считать полученную работу идущую на нагревание воды.

Answer 1

Дано:                           Решение:

m= 25 кг              ν=Aпол/Асов

T= 25                   Aпол=cmT - работа, затраченная на нагревание воды

Tк=100                Асов=Pt - работа, затраченная на нагрев чайника

t=6 мин=360 с   ν=cmT/Pt = 4200*2*75/2000*360=0.875=87.5%

P=2 кВт

Найти:

ν-?

Answer 2

Problem Analysis

We are given the following information: - Mass of water: 2 kg - Initial temperature of water: 25 degrees Celsius - Final temperature of water (boiling point): 100 degrees Celsius - Time taken to heat the water: 6 minutes - Power of the electric kettle: 2 kW

We need to find the efficiency (or thermal efficiency) of the electric kettle.

Solution

To find the efficiency of the electric kettle, we need to calculate the work done and the energy input.

# Step 1: Calculate the energy input

The energy input can be calculated using the formula:

Energy input = Power x Time

Given that the power of the electric kettle is 2 kW and the time taken to heat the water is 6 minutes, we can calculate the energy input as follows:

Energy input = 2 kW x 6 minutes

Note: We need to convert the time from minutes to seconds, as the power is given in kilowatts.

# Step 2: Calculate the work done

The work done can be calculated using the formula:

Work done = Mass x Specific heat capacity x Change in temperature

The specific heat capacity of water is approximately 4.18 J/g°C.

Given that the mass of water is 2 kg, the initial temperature is 25 degrees Celsius, and the final temperature is 100 degrees Celsius, we can calculate the change in temperature as follows:

Change in temperature = Final temperature - Initial temperature

Now we can calculate the work done using the formula mentioned above.

# Step 3: Calculate the efficiency

The efficiency of the electric kettle can be calculated using the formula:

Efficiency = (Work done / Energy input) x 100

Now we can substitute the values we calculated in the previous steps to find the efficiency.

Calculation

Let's calculate the efficiency of the electric kettle using the given information.

# Step 1: Calculate the energy input

Energy input = 2 kW x 6 minutes = 12 kWh

# Step 2: Calculate the work done

Change in temperature = 100°C - 25°C = 75°C

Work done = 2 kg x 4.18 J/g°C x 75°C = 627 J

# Step 3: Calculate the efficiency

Efficiency = (Work done / Energy input) x 100 = (627 J / 12 kWh) x 100

Note: We need to convert the energy input from kilowatt-hours (kWh) to joules (J) to have consistent units.

Answer

The efficiency of the electric kettle is approximately 0.005225%.

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