Question

Задача 1: Сколько каменного угля требуется, чтобы полностью расплавить железную болванку массой 15 кг. Начальная температура болванки + 20°С. Задача 2: Сколько природного газа требуется, чтобы полностью расплавить алюминиевую заготовку массой 10 кг. Начальная температура заготовки + 25°С.

Answer 1

Чтобы расплавить вещество, нужна теплота для его нагревания и плавления. Все это вместе равно теплоте сгорания топлива, т.к. никаких потерь не происходит, т.е.:

Qсгорания=Qнагр+Qплав

Ответ во вложении.

Answer 2

Task 1: Сколько каменного угля требуется, чтобы полностью расплавить железную болванку массой 15 кг. Начальная температура болванки 20°C.

To calculate the amount of coal required to completely melt the iron ingot, we need to consider the specific heat capacity of iron and the heat required for melting.

The specific heat capacity of iron is approximately 0.45 J/g°C [[1]]. This means that it takes 0.45 Joules of energy to raise the temperature of 1 gram of iron by 1 degree Celsius.

To melt the iron ingot, we need to raise its temperature from 20°C to its melting point, which is approximately 1538°C for iron [[2]]. This means we need to increase the temperature by 1538 - 20 = 1518°C.

The mass of the iron ingot is given as 15 kg.

To calculate the heat required to raise the temperature of the iron ingot, we can use the formula:

Q = m * c * ΔT

Where: - Q is the heat required (in Joules) - m is the mass of the iron ingot (in grams) - c is the specific heat capacity of iron (in J/g°C) - ΔT is the change in temperature (in °C)

Let's calculate the heat required:

Q = 15,000 g * 0.45 J/g°C * 1518°C

Calculating this, we find that the heat required is approximately 10,267,500 Joules.

Now, let's find out how much coal is required to produce this amount of heat.

The calorific value of coal, which is the amount of heat energy released per unit mass of coal, varies depending on the type of coal. Let's assume an average calorific value of 24 MJ/kg for coal [[3]].

To calculate the mass of coal required, we can use the formula:

Q = m * CV

Where: - Q is the heat required (in Joules) - m is the mass of coal (in kilograms) - CV is the calorific value of coal (in J/kg)

Let's calculate the mass of coal required:

10,267,500 J = m * 24,000,000 J/kg

Simplifying this equation, we find that the mass of coal required is approximately 0.427 kg.

Therefore, approximately 0.427 kg of coal is required to completely melt the 15 kg iron ingot.

[[1]] Source: [Engineering Toolbox - Specific Heat Capacity of Metals Table](https://www.engineeringtoolbox.com/specific-heat-capacity-metals-d_152.html) [[2]] Source: [Engineering Toolbox - Melting Points of Elements Reference](https://www.engineeringtoolbox.com/melting-points-elements-reference-d_1266.html) [[3]] Source: [World Coal Association - Coal and Electricity](https://www.worldcoal.org/coal/uses-coal/coal-electricity)