Question

Для определения температуры в печи нагретый в ней стальной болт массой 0,3 кг бросили в медный сосуд массой 0,2 кг , содержащий 1,2 кг воды при 15 градусов С .Температура воды повысилась да 32 градусов С. Вычислите температуру печи.

Answer 1

Болт отдает тепло, вода и медный сосуд принимаютQ1==c1m1(t1-t)- охлаждение стального болтаQ2=c2m2(t-t2)-нагревание сосуда до общей температуры Q3=c3m3(t-t2)-нагревание воды до общей температурыQ1=Q2+Q3-уравнение теплового баланса 500*0,3*(t1-32)=400*0,2*(32-15)+4200*1,2*(32-15)150(t1-32)=87040t1-32=87040/150=580t1=580+32=612 градусов Ц.

Answer 2

Problem Analysis

To determine the temperature of the oven, we can use the principle of conservation of energy. The heat gained by the water and the copper vessel is equal to the heat lost by the steel bolt. We can use the equation:

Q_water + Q_copper = Q_steel

Where: - Q_water is the heat gained by the water - Q_copper is the heat gained by the copper vessel - Q_steel is the heat lost by the steel bolt

We can calculate the heat gained by the water using the equation:

Q_water = m_water * c_water * ΔT_water

Where: - m_water is the mass of the water - c_water is the specific heat capacity of water - ΔT_water is the change in temperature of the water

We can calculate the heat gained by the copper vessel using the equation:

Q_copper = m_copper * c_copper * ΔT_copper

Where: - m_copper is the mass of the copper vessel - c_copper is the specific heat capacity of copper - ΔT_copper is the change in temperature of the copper vessel

We can calculate the heat lost by the steel bolt using the equation:

Q_steel = m_steel * c_steel * ΔT_steel

Where: - m_steel is the mass of the steel bolt - c_steel is the specific heat capacity of steel - ΔT_steel is the change in temperature of the steel bolt

By equating the heat gained and lost, we can solve for the temperature of the oven.

Solution

Given: - Mass of the steel bolt (m_steel) = 0.3 kg - Mass of the copper vessel (m_copper) = 0.2 kg - Mass of the water (m_water) = 1.2 kg - Initial temperature of the water (T_water_initial) = 15°C - Final temperature of the water (T_water_final) = 32°C

To calculate the temperature of the oven, we need to determine the change in temperature of the copper vessel and the steel bolt.

First, let's calculate the heat gained by the water:

Q_water = m_water * c_water * ΔT_water

Using the specific heat capacity of water (c_water = 4186 J/kg°C), we can calculate:

Q_water = 1.2 kg * 4186 J/kg°C * (32°C - 15°C)

Next, let's calculate the heat gained by the copper vessel:

Q_copper = m_copper * c_copper * ΔT_copper

The specific heat capacity of copper (c_copper) is not provided in the question. We will assume a value of 385 J/kg°C, which is the average specific heat capacity of copper.

Q_copper = 0.2 kg * 385 J/kg°C * ΔT_copper

Now, let's calculate the heat lost by the steel bolt:

Q_steel = m_steel * c_steel * ΔT_steel

The specific heat capacity of steel (c_steel) is not provided in the question. We will assume a value of 500 J/kg°C, which is the average specific heat capacity of steel.

Q_steel = 0.3 kg * 500 J/kg°C * ΔT_steel

Since the heat gained by the water and the copper vessel is equal to the heat lost by the steel bolt, we can set up the equation:

Q_water + Q_copper = Q_steel

Substituting the calculated values:

1.2 kg * 4186 J/kg°C * (32°C - 15°C) + 0.2 kg * 385 J/kg°C * ΔT_copper = 0.3 kg * 500 J/kg°C * ΔT_steel

Simplifying the equation:

1.2 * 4186 * 17 + 0.2 * 385 * ΔT_copper = 0.3 * 500 * ΔT_steel

ΔT_copper = (1.2 * 4186 * 17) / (0.2 * 385) - ΔT_steel

Now, let's solve for ΔT_steel:

1.2 * 4186 * 17 + 0.2 * 385 * [(1.2 * 4186 * 17) / (0.2 * 385) - ΔT_steel] = 0.3 * 500 * ΔT_steel

Simplifying the equation:

1.2 * 4186 * 17 + 0.2 * 385 * (1.2 * 4186 * 17) / (0.2 * 385) - 0.2 * 385 * ΔT_steel = 0.3 * 500 * ΔT_steel

1.2 * 4186 * 17 + 1.2 * 4186 * 17 - 0.2 * 385 * ΔT_steel = 0.3 * 500 * ΔT_steel

2.4 * 4186 * 17 - 0.2 * 385 * ΔT_steel = 0.3 * 500 * ΔT_steel

2.4 * 4186 * 17 = (0.3 * 500 + 0.2 * 385) * ΔT_steel

ΔT_steel = (2.4 * 4186 * 17) / (0.3 * 500 + 0.2 * 385)

Now that we have the value of ΔT_steel, we can calculate the temperature of the oven:

T_oven = T_water_final + ΔT_steel

Substituting the values:

T_oven = 32°C + [(2.4 * 4186 * 17) / (0.3 * 500 + 0.2 * 385)]

Let's calculate the temperature of the oven using the given values.

Calculation

Using the given values: - Mass of the steel bolt (m_steel) = 0.3 kg - Mass of the copper vessel (m_copper) = 0.2 kg - Mass of the water (m_water) = 1.2 kg - Initial temperature of the water (T_water_initial) = 15°C - Final temperature of the water (T_water_final) = 32°C - Specific heat capacity of water (c_water) = 4186 J/kg°C - Specific heat capacity of copper (c_copper) = 385 J/kg°C - Specific heat capacity of steel (c_steel) = 500 J/kg°C

Let's calculate the temperature of the oven:

Q_water = 1.2 kg * 4186 J/kg°C * (32°C - 15°C) = 1.2 * 4186 * 17 = 85747.2 J

Q_copper = 0.2 kg * 385 J/kg°C * ΔT_copper

Q_steel = 0.3 kg * 500 J/kg°C * ΔT_steel

Q_water + Q_copper = Q_steel

85747.2 J + 0.2 kg * 385 J/kg°C * ΔT_copper = 0.3 kg * 500 J/kg°C * ΔT_steel

ΔT_copper = (85747.2 J) / (0.2 * 385 J/kg°C) - ΔT_steel

ΔT_copper = 222.8°C - ΔT_steel

85747.2 J + 0.2 kg * 385 J/kg°C * (222.8°C - ΔT_steel) = 0.3 kg * 500 J/kg°C * ΔT_steel

85747.2 J + 0.2 * 385 * (222.8 - ΔT_steel) = 0.3 * 500 * ΔT_steel

85747.2 J + 0.2 * 385 * 222.8 - 0.2 * 385 * ΔT_steel = 0.3 * 500 * ΔT_steel

85747.2 J + 0.2 * 385 * 222.8 = 0.3 * 500 * ΔT_steel + 0.2 * 385 * ΔT_steel

85747.2 J + 0.2 * 385 * 222.8 = (0.3 * 500 + 0.2 * 385) * ΔT_steel

ΔT_steel = (85747.2 J + 0.2 * 385 * 222.8) / (0.3 * 500 + 0.2 * 385)

ΔT_steel = 85747.2 J + 0.2 * 385 * 222.8 / (0.3 * 500 + 0.2 * 385)

ΔT_steel ≈ 68.8°C

T_oven = T_water_final + ΔT_steel

T_oven = 32°C + 68.8°C

T_oven ≈ 100.8°C

Answer

The temperature of the oven is approximately 100.8°C.