Question

Какую массу керосина нужно сжечь в примусе с КПД П = 40%, чтобы расплавить m = 4 кг льда, взятого при температуре -10 °С, если удельная теплота сгорания керосина q=42000кДЖ/кг?

Answer 1

$n=\frac{cm_1t+hm_1}{qm_2}$

$m_2=\frac{cm_1t+hm_1}{qn}$

$m_2=\frac{2100Dg/kgC*4kg*10C+340000Dg/kg*4kg}{42000000Dg/kg*0.4} \approx 0.085kg$

Ответ: 0.085кг

Answer 2

Сначала лёд нужно нагреть до температуры плавления

 

Q=cmΔt

 

c=2100

 

m=4

 

Δt=10

 

Q=4*2100*10=84000 Дж

 

Потом плавление

 

Q=λ*m=330000*4=1320000 Дж

 

λ - Удельная теплота плавления льда 

 

m - масса

 

Всего для плавления льда понадобиться

 

Q=1320000+84000=1404000 Дж

 

С учётом КПД 

 

Q=1404000/0,4=3510000 Дж

 

Теперь ищем массу керосина

 

Q=q*m

 

$m=\frac{Q}{q}$

 

$m=\frac{3510000}{42000000}\approx0,0835$ кг

Answer 3

Calculation of the Mass of Kerosene Required to Melt Ice

To calculate the mass of kerosene required to melt a given mass of ice, we need to consider the specific heat capacity of ice, the heat of fusion, and the efficiency of the stove.

Given: - Mass of ice, m = 4 kg - Initial temperature of ice, T1 = -10 °C - Efficiency of the stove, η = 40% (or 0.4) - Heat of combustion of kerosene, q = 42000 kJ/kg

To melt the ice, we need to raise its temperature from -10 °C to 0 °C and then provide the heat of fusion to convert it from solid to liquid.

Calculation Steps:

1. Calculate the heat required to raise the temperature of the ice from -10 °C to 0 °C using the specific heat capacity of ice: - The specific heat capacity of ice, c = 2.09 kJ/kg°C. - The temperature change, ΔT = 0 °C - (-10 °C) = 10 °C. - The heat required for this temperature change is given by: Q1 = m * c * ΔT.

2. Calculate the heat required for the phase change from solid to liquid using the heat of fusion: - The heat of fusion of ice, L = 334 kJ/kg. - The heat required for this phase change is given by: Q2 = m * L.

3. Calculate the total heat required to melt the ice: - The total heat required is given by: Q_total = Q1 + Q2.

4. Calculate the energy input to the stove: - The energy input to the stove is given by: Q_input = Q_total / η.

5. Calculate the mass of kerosene required: - The mass of kerosene required is given by: m_kerosene = Q_input / q.

Let's calculate the mass of kerosene required using the given values.

Calculation:

1. Calculate the heat required to raise the temperature of the ice: - c = 2.09 kJ/kg°C - ΔT = 10 °C - Q1 = m * c * ΔT = 4 kg * 2.09 kJ/kg°C * 10 °C = 83.6 kJ.

2. Calculate the heat required for the phase change: - L = 334 kJ/kg - Q2 = m * L = 4 kg * 334 kJ/kg = 1336 kJ.

3. Calculate the total heat required to melt the ice: - Q_total = Q1 + Q2 = 83.6 kJ + 1336 kJ = 1420.6 kJ.

4. Calculate the energy input to the stove: - Q_input = Q_total / η = 1420.6 kJ / 0.4 = 3551.5 kJ.

5. Calculate the mass of kerosene required: - m_kerosene = Q_input / q = 3551.5 kJ / 42000 kJ/kg = 0.0846 kg (rounded to four decimal places).

Therefore, approximately 0.0846 kg of kerosene is required to melt 4 kg of ice taken at a temperature of -10 °C, assuming an efficiency of 40% and a heat of combustion of kerosene of 42000 kJ/kg.

Please note that this calculation assumes ideal conditions and does not account for heat losses or other factors that may affect the actual amount of kerosene required.