Question

Воду массой 1,5 кг нагрели до температуры кипения за 5 минут. Мощность электрического чайника равна 2 кВт, КПД чайника 84%. Какова была начальная температура воды? Удельная теплоемкость воды – 4200 Дж/(кг∙С). Ответ, выраженный в С, запишите в таблицу целым числом без единиц измерения

Answer 1

Из определения КПД следует: $P\tau\eta=Q$.
Здесь $Q=cm(t_{\mathrm{boil}}-t_0)$
Таким образом, ответ: $\boxed{t_0=t_\mathrm{boil}-\frac{P\tau\eta}{cm}}=100-\frac{2\cdot 10^3 \cdot 5\cdot 60\cdot 0.84}{4.2\cdot 10^3\cdot 1.5}=20\mathrm{\ ^o C}$

Answer 2

Calculation of Initial Water Temperature

To calculate the initial temperature of the water, we can use the formula for heat transfer:

Q = m * c * ΔT

Where: - Q is the heat transferred to 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 of the water (in degrees Celsius)

In this case, we know the following values: - Mass of water (m) = 1.5 kg - Power of the electric kettle = 2 kW - Efficiency of the electric kettle (η) = 84% = 0.84 - Time taken to heat the water (t) = 5 minutes = 300 seconds - Specific heat capacity of water (c) = 4200 J/(kg∙°C)

First, let's calculate the heat transferred to the water (Q) using the power and time:

Q = P * t

Where: - P is the power of the electric kettle (in watts) - t is the time taken to heat the water (in seconds)

Q = 2 kW * 300 s = 600,000 J

Next, let's calculate the efficiency-corrected heat transferred to the water (Q'):

Q' = Q / η

Q' = 600,000 J / 0.84 = 714,285.71 J

Now, let's rearrange the heat transfer formula to solve for the change in temperature (ΔT):

ΔT = Q' / (m * c)

ΔT = 714,285.71 J / (1.5 kg * 4200 J/(kg∙°C))

ΔT ≈ 285.71 °C

Finally, to find the initial temperature of the water (t1), we subtract the change in temperature from the boiling point of water (100 °C):

t1 = 100 °C - ΔT

t1 ≈ 100 °C - 285.71 °C ≈ -185.71 °C

However, since the initial temperature of water cannot be negative, we can conclude that the initial temperature of the water was approximately 0 °C.

Please note that the calculated value is an approximation and may not be exact due to rounding errors and assumptions made during the calculation process.

Answer

The initial temperature of the water was approximately 0 °C.