Question

Кусок льда массой 700 г поместили в воду. масса воды =2.5 кг, начальная температура воды =5°c. Когда установилось тепловое равновесие оказалось что масса льда увеличилась на 64 г. Определите начальную температуру льда)Помогите плиз!Физика

Answer 1

-1,-2градуса кажется таким образом ☺

Answer 2

Problem Analysis

We have a piece of ice with a mass of 700 g that is placed in water. The mass of the water is 2.5 kg, and the initial temperature of the water is 5°C. After reaching thermal equilibrium, it is found that the mass of the ice has increased by 64 g. We need to determine the initial temperature of the ice.

Solution

To solve this problem, we can use the principle of conservation of energy. The heat gained by the ice is equal to the heat lost by the water. We can calculate the heat gained by the ice using the formula:

Q_ice = m_ice * c_ice * (T_final - T_initial)

where: - Q_ice is the heat gained by the ice - m_ice is the mass of the ice (700 g + 64 g) - c_ice is the specific heat capacity of ice - T_final is the final temperature of the ice (0°C) - T_initial is the initial temperature of the ice (unknown)

We can calculate the heat lost by the water using the formula:

Q_water = m_water * c_water * (T_initial - T_final)

where: - Q_water is the heat lost by the water - m_water is the mass of the water (2.5 kg) - c_water is the specific heat capacity of water - T_initial is the initial temperature of the water (5°C) - T_final is the final temperature of the water (unknown)

Since the heat gained by the ice is equal to the heat lost by the water, we can set up the equation:

Q_ice = Q_water

Substituting the formulas for Q_ice and Q_water, we get:

m_ice * c_ice * (T_final - T_initial) = m_water * c_water * (T_initial - T_final)

Simplifying the equation, we have:

m_ice * c_ice * T_final - m_ice * c_ice * T_initial = m_water * c_water * T_initial - m_water * c_water * T_final

Rearranging the equation, we get:

(m_ice * c_ice + m_water * c_water) * T_final = (m_ice * c_ice + m_water * c_water) * T_initial

Finally, solving for T_initial, we have:

T_initial = (m_ice * c_ice * T_final + m_water * c_water * T_final) / (m_ice * c_ice + m_water * c_water)

Now, let's substitute the known values and calculate the initial temperature of the ice.

Calculation

Given: - Mass of ice (m_ice) = 700 g + 64 g = 764 g = 0.764 kg - Mass of water (m_water) = 2.5 kg - Initial temperature of water (T_initial) = 5°C - Final temperature of ice and water (T_final) = 0°C

Using the specific heat capacities of ice and water: - Specific heat capacity of ice (c_ice) = 2.09 J/g°C- Specific heat capacity of water (c_water) = 4.18 J/g°C Substituting the values into the equation:

T_initial = (m_ice * c_ice * T_final + m_water * c_water * T_final) / (m_ice * c_ice + m_water * c_water)

T_initial = (0.764 kg * 2.09 J/g°C * 0°C + 2.5 kg * 4.18 J/g°C * 0°C) / (0.764 kg * 2.09 J/g°C + 2.5 kg * 4.18 J/g°C)

Calculating the numerator:

0.764 kg * 2.09 J/g°C * 0°C + 2.5 kg * 4.18 J/g°C * 0°C = 0 J

Calculating the denominator:

0.764 kg * 2.09 J/g°C + 2.5 kg * 4.18 J/g°C = 3.161 kg * J/g°C

Finally, calculating T_initial:

T_initial = 0 J / 3.161 kg * J/g°C = 0°C

Therefore, the initial temperature of the ice is 0°C.

Answer

The initial temperature of the ice is 0°C.

References

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