Find the mass of water that vaporizes when 4.04 kg of mercury at 210 °C is added to 0.498 kg of water at 81.6 °C.
To find the mass of water that vaporizes, we need to calculate the heat transferred between the mercury and the water.
The heat transferred during a phase change can be calculated using the equation:
Q = m * L
Where:
- Q is the heat transferred
- m is the mass of the substance that undergoes the phase change
- L is the heat of vaporization of the substance
In this case, the heat transferred from the water to the mercury will cause the water to vaporize. Therefore, we need to calculate the heat transferred from the water to the mercury first.
First, let's calculate the heat transferred from the water:
Q_water = m_water * c_water * ΔT_water
Where:
- Q_water is the heat transferred from the water
- 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
The specific heat capacity of water is approximately 4.18 J/g°C.
Now, let's calculate the heat transferred from the water to the mercury:
Q_water_to_mercury = -Q_water
Since energy is conserved, the heat transferred from the water to the mercury will be equal to the heat gained by the mercury, but with the opposite sign.
Next, let's calculate the heat transferred to the mercury:
Q_mercury = m_mercury * c_mercury * ΔT_mercury
Where:
- Q_mercury is the heat transferred to the mercury
- m_mercury is the mass of the mercury
- c_mercury is the specific heat capacity of mercury
- ΔT_mercury is the change in temperature of the mercury
The specific heat capacity of mercury is approximately 0.14 J/g°C.
Finally, to calculate the mass of water that vaporizes, we need to consider the heat of vaporization of water:
Q_vaporization = m_vaporized_water * L_water
Where:
- Q_vaporization is the heat transferred during the phase change from liquid water to vapor
- m_vaporized_water is the mass of the water that vaporizes
- L_water is the heat of vaporization of water
The heat of vaporization of water is approximately 2257 J/g.
Using the given values, we can now calculate the mass of water that vaporizes.