Question

Алюмінієву кулю, нагріту до 140°С, занурили в олію, маса якої у два рази більша за масу кулі. Теплова рівновага встановилась за температури 40°С. Визначте початкову температуру олії (у °С). Питома теплоємність алюмінію 880 Дж/(кг·°С), олії - 2000 Дж/(кг·°С

Answer 1

Ответ:

Начальная температура масла равна 18°С.

Объяснение:

Алюминиевый шар, нагретый до 140°С, погрузили в масло, масса которого в два раза больше массы шара. Тепловое равновесие установилось при температуре 40°С. Определите начальную температуру масла (°С). Удельная теплоемкость алюминия 880 Дж/(кг·°С), масла - 2000 Дж/(кг·°С)

Дано:

t₁ = 140°С

m₂ = 2m₁

t = 40°С

c₁ = 880 Дж/(кг·°С)

c₂ = 2000 Дж/(кг·°С)

t₂-?

——————————————

Уравнение теплового баланса:

$Q_1 = Q_2$

Количество теплоты, отданное алюминиевым шаром:

$Q_1 = m_1c_1(t_1 - t)$

Количество теплоты, полученное маслом:

$Q_2 = m_2c_2(t - t_2)$

Приравняем и заменим m₂ = 2m₁:

$m_1c_1(t_1 - t) = 2m_1c_2(t - t_2)$

Сократим массу:

$c_1(t_1 - t) = 2c_2(t - t_2)$

Отсюда:

$t_2 = t - \dfrac{c_1(t_1 - t)}{2c_2}$

Расчет:

t₂ = 40°С - 880 Дж/(кг·°С) (140°С - 40°С) / (2·2000 Дж/(кг·°С)) = 40°С - 88000 Дж/кг / (4000 Дж/(кг·°С)) = 40°С - 22°С = 18°С

#SPJ1

Answer 2

Understanding the problem

We have an aluminum sphere that is heated to a temperature of 140°C and then submerged in oil. The mass of the oil is twice the mass of the sphere. After reaching a thermal equilibrium, the temperature of the oil is 40°C. We need to determine the initial temperature of the oil.

Solution

To solve this problem, we can use the principle of heat transfer and energy conservation. The heat lost by the aluminum sphere is equal to the heat gained by the oil. We can calculate the heat lost by the aluminum sphere and then equate it to the heat gained by the oil.

The heat lost by the aluminum sphere can be calculated using the formula:

Q_loss = m_aluminum * c_aluminum * (T_initial - T_final)

Where: - Q_loss is the heat lost by the aluminum sphere - m_aluminum is the mass of the aluminum sphere - c_aluminum is the specific heat capacity of aluminum - T_initial is the initial temperature of the aluminum sphere - T_final is the final temperature of the aluminum sphere (which is 40°C)

The heat gained by the oil can be calculated using the formula:

Q_gain = m_oil * c_oil * (T_final - T_initial)

Where: - Q_gain is the heat gained by the oil - m_oil is the mass of the oil - c_oil is the specific heat capacity of the oil - T_initial is the initial temperature of the oil - T_final is the final temperature of the oil (which is also 40°C)

Since the mass of the oil is twice the mass of the aluminum sphere, we can write:

m_oil = 2 * m_aluminum

We can now set up the equation by equating the heat lost by the aluminum sphere to the heat gained by the oil:

m_aluminum * c_aluminum * (T_initial - T_final) = 2 * m_aluminum * c_oil * (T_final - T_initial)

Now we can solve this equation for T_initial, the initial temperature of the oil.

Calculation

Given: - Specific heat capacity of aluminum (c_aluminum) = 880 J/(kg·°C) - Specific heat capacity of oil (c_oil) = 2000 J/(kg·°C) - Final temperature of the aluminum sphere and oil (T_final) = 40°C

Let's assume the mass of the aluminum sphere (m_aluminum) is 1 kg. Then the mass of the oil (m_oil) would be 2 kg.

Substituting the values into the equation, we get:

1 * 880 * (T_initial - 40) = 2 * 1 * 2000 * (40 - T_initial)

Simplifying the equation:

880 * (T_initial - 40) = 4000 * (40 - T_initial)

Expanding and rearranging the equation:

880 * T_initial - 880 * 40 = 4000 * 40 - 4000 * T_initial

880 * T_initial + 4000 * T_initial = 4000 * 40 + 880 * 40

4880 * T_initial = 4000 * 40 + 880 * 40

T_initial = (4000 * 40 + 880 * 40) / 4880

Calculating the value of T_initial:

T_initial = 320000 / 4880 ≈ 65.57°C

Therefore, the initial temperature of the oil is approximately 65.57°C.