Question

Кипятильник потребляет ток силой I=5.0 A при напряжении U=220 B. За какое время этот кипятильник нагреет воду объёмом V=0.20 л от температуры t=23°С до кипения, если КПД кипятильника η=60% (Удельная теплоёмкость воды c=4200 Дж/кг*°С, плотность воды ρ=1000 кг/м3, температура кипения воды tk=100°С.)

Answer 1

Дано:
I=5A
U=220B
V=0.0002 м³
ρ=1000 кг/м³
η=0,6
с=4200 Дж/кг°С
t=77°С
T=?
Решение:
Q₁=mct
m=ρV
Q₁=Qη
Q=Q₁/η
Q=PT
P=UI, тогда
UIT=mct/η⇒T=ρVct/ηUI=1000*0.0002*4200*77/0.6*5*220=660c=11минут
Ответ: Т =11 минут

Answer 2

Calculation of the Time Required to Heat the Water

To calculate the time required for the kettle to heat the water from 23°C to boiling point (100°C), we can use the formula:

Q = m * c * ΔT

Where: - Q is the amount of heat energy required to heat the water (in Joules) - m is the mass of the water (in kilograms) - c is the specific heat capacity of water (in Joules per kilogram per degree Celsius) - ΔT is the change in temperature (in degrees Celsius)

In this case, the mass of the water is given as 0.20 liters, which we need to convert to kilograms. The density of water is 1000 kg/m³, so the mass of the water can be calculated as:

m = V * ρ

Where: - V is the volume of the water (in liters) - ρ is the density of water (in kilograms per cubic meter)

Let's calculate the mass of the water:

m = 0.20 kg * 1000 kg/m³ = 200 kg

Now, we can calculate the amount of heat energy required to heat the water:

Q = m * c * ΔT

The specific heat capacity of water is given as 4200 J/kg°C, and the change in temperature is:

ΔT = tk - t = 100°C - 23°C = 77°C

Substituting the values into the formula, we get:

Q = 200 kg * 4200 J/kg°C * 77°C = 6,468,000 J

Next, we need to calculate the power consumed by the kettle. The power (P) is given by the formula:

P = I * U

Where: - P is the power consumed by the kettle (in Watts) - I is the current (in Amperes) - U is the voltage (in Volts)

In this case, the current is given as 5.0 A and the voltage is given as 220 V. Substituting the values into the formula, we get:

P = 5.0 A * 220 V = 1100 W

Now, we can calculate the time required to heat the water using the formula:

t = Q / (P * η)

Where: - t is the time required to heat the water (in seconds) - Q is the amount of heat energy required to heat the water (in Joules) - P is the power consumed by the kettle (in Watts) - η is the efficiency of the kettle (expressed as a decimal)

In this case, the efficiency of the kettle is given as 60%, which can be expressed as 0.60. Substituting the values into the formula, we get:

t = 6,468,000 J / (1100 W * 0.60) = 9,480 seconds

Therefore, the kettle will take approximately 9,480 seconds, or about 2 hours and 38 minutes, to heat the water from 23°C to boiling point.

Please note that this calculation assumes that the kettle operates at a constant power and efficiency throughout the heating process.