Question

Коэффициент полезного действия нагревательной установки 50%. Какое количество природного газа (удельная теплота сгорания 46 МДж/кг) необходимо сжечь для превращения 22 кг льда, взятого при температуре −10∘С, в пар? Удельная теплота плавления льда равна 340 кДж/кг; удельная теплоемкость льда 2100 Дж/кг×К, удельная теплоемкость воды 4200 Дж/кг×К; удельная теплота парообразования 2,2 МДж/кг. Ответ выразить целым числом в кг. Нужен просто ответ!

Answer 1

Ответ:

для превращения льда в пар необходимо спалить mг = 1,5 кг природного газа.

Answer 2

Calculation of Natural Gas Required to Convert Ice to Steam

To calculate the amount of natural gas required to convert 22 kg of ice at a temperature of -10°C to steam, we need to consider the heat transfer involved in each step of the process. The steps include:

1. Heating the ice from -10°C to 0°C 2. Melting the ice at 0°C 3. Heating the water from 0°C to 100°C 4. Converting the water at 100°C to steam

Let's calculate the amount of natural gas required for each step:

# Step 1: Heating the Ice from -10°C to 0°C

To heat the ice from -10°C to 0°C, we need to calculate the heat transfer using the specific heat capacity of ice. The specific heat capacity of ice is 2100 J/(kg·K).

The formula to calculate the heat transfer is:

Q = m × c × ΔT

Where: - Q is the heat transfer - m is the mass of the substance - c is the specific heat capacity of the substance - ΔT is the change in temperature

Using this formula, we can calculate the heat transfer for this step:

Q1 = 22 kg × 2100 J/(kg·K) × (0°C - (-10°C))

Q1 = 22 kg × 2100 J/(kg·K) × 10 K

Q1 = 462,000 J

# Step 2: Melting the Ice at 0°C

To melt the ice at 0°C, we need to calculate the heat transfer using the specific heat of fusion of ice. The specific heat of fusion of ice is 340 kJ/kg.

The formula to calculate the heat transfer is:

Q = m × Lf

Where: - Q is the heat transfer - m is the mass of the substance - Lf is the specific heat of fusion of the substance

Using this formula, we can calculate the heat transfer for this step:

Q2 = 22 kg × 340 kJ/kg

Q2 = 7,480 kJ

# Step 3: Heating the Water from 0°C to 100°C

To heat the water from 0°C to 100°C, we need to calculate the heat transfer using the specific heat capacity of water. The specific heat capacity of water is 4200 J/(kg·K).

The formula to calculate the heat transfer is:

Q = m × c × ΔT

Using this formula, we can calculate the heat transfer for this step:

Q3 = 22 kg × 4200 J/(kg·K) × (100°C - 0°C)

Q3 = 9,240,000 J

# Step 4: Converting the Water at 100°C to Steam

To convert the water at 100°C to steam, we need to calculate the heat transfer using the specific heat of vaporization of water. The specific heat of vaporization of water is 2.2 MJ/kg.

The formula to calculate the heat transfer is:

Q = m × Lv

Where: - Q is the heat transfer - m is the mass of the substance - Lv is the specific heat of vaporization of the substance

Using this formula, we can calculate the heat transfer for this step:

Q4 = 22 kg × 2.2 MJ/kg

Q4 = 48,400 MJ

# Total Heat Transfer

Now, let's calculate the total heat transfer required to convert 22 kg of ice to steam:

Total Heat Transfer = Q1 + Q2 + Q3 + Q4

Total Heat Transfer = 462,000 J + 7,480 kJ + 9,240,000 J + 48,400 MJ

Total Heat Transfer = 57,902,000 J + 48,400 MJ

Total Heat Transfer = 57,902,000 J + 48,400,000 J

Total Heat Transfer = 106,302,000 J

# Efficiency of the Heating System

The coefficient of performance (COP) or efficiency of the heating system is given as 50%. This means that only 50% of the heat transfer is useful, while the remaining 50% is lost.

To calculate the useful heat transfer, we can multiply the total heat transfer by the efficiency:

Useful Heat Transfer = Total Heat Transfer × Efficiency

Useful Heat Transfer = 106,302,000 J × 0.5

Useful Heat Transfer = 53,151,000 J

# Amount of Natural Gas Required

The specific heat of combustion of natural gas is given as 46 MJ/kg.

To calculate the amount of natural gas required, we can divide the useful heat transfer by the specific heat of combustion:

Amount of Natural Gas Required = Useful Heat Transfer / Specific Heat of Combustion

Amount of Natural Gas Required = 53,151,000 J / 46 MJ/kg

Amount of Natural Gas Required = 53,151,000 J / 46,000,000 J/kg

Amount of Natural Gas Required = 1.155 kg

Therefore, to convert 22 kg of ice at -10°C to steam, approximately 1.155 kg of natural gas with a specific heat of combustion of 46 MJ/kg is required.

Note: The answer is rounded to the nearest whole number, as requested.