A glass flask with a mass ok 3.00kg and volume of 1000 cm3 is completely filled with mercury and is at a temperature of 55.0oC. The flask is then lowered into an ice water bath. After thermal equilibrium is reached, (a) what percentage of the flask will be filled with mercury? (b) How much ice will melt lowering the temperature of the flask and mercury?
(density of mercury is 13.56 g/cm3)
To calculate the percentage of the flask that will be filled with mercury after thermal equilibrium is reached, we need to consider the change in volume of the mercury due to the change in temperature.
(a) To find the final volume of the mercury, we need to use the coefficient of thermal expansion of mercury. The formula to calculate the change in volume of a substance with respect to temperature change is given by:
ΔV = V₀ * β * ΔT
where ΔV is the change in volume, V₀ is the initial volume, β is the coefficient of thermal expansion, and ΔT is the change in temperature.
The coefficient of thermal expansion of mercury is approximately 0.000181 (1/°C).
Given:
Initial volume (V₀) = 1000 cm³
Change in temperature (ΔT) = (0 °C - 55 °C) = -55 °C
Coefficient of thermal expansion (β) = 0.000181 (1/°C)
Using the formula, we can find the change in volume of the mercury:
ΔV = 1000 cm³ * 0.000181 (1/°C) * (-55 °C)
= -9.955 cm³ (rounded to three decimal places)
Since the volume cannot be negative, we take the absolute value of the change in volume:
|ΔV| = 9.955 cm³
The final volume of the mercury is the sum of the initial volume and the change in volume:
V_final = V₀ + ΔV
= 1000 cm³ + 9.955 cm³
= 1009.955 cm³ (rounded to three decimal places)
Now we can calculate the percentage of the flask that will be filled with mercury:
Percentage = (V_final / V₀) * 100
= (1009.955 cm³ / 1000 cm³) * 100
≈ 100.995% (rounded to three decimal places)
Therefore, approximately 101% of the flask will be filled with mercury after thermal equilibrium is reached.
(b) To calculate the amount of ice that will melt due to the temperature change, we need to consider the heat transfer between the flask and the ice.
The heat transfer can be calculated using the formula:
Q = m * c * ΔT
where Q is the heat transfer, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
The heat transferred from the flask to the ice will be equal to the heat gained by the ice, which can be calculated as:
Q_ice = Q_flask
Given:
Mass of the flask (m_flask) = 3.00 kg
Specific heat capacity of water (c_water) = 4.18 J/(g·°C) (assuming the ice bath is made of water)
Change in temperature (ΔT) = -55 °C
First, we need to convert the mass of the flask to grams:
m_flask = 3.00 kg * 1000 g/kg
= 3000 g
Using the formula, we can find the heat transfer:
Q_flask = m_flask * c_water * ΔT
= 3000 g * 4.18 J/(g·°C) * (-55 °C)
= -691,950 J (rounded to three decimal places)
Thus, the amount of ice that will melt due to the temperature change is approximately 691,950 J.