A glass bottle full of mercury has 500g on being heated through 35 degree, 2.43g of mercury are expelled. calculate the mass of mercury remaining in the bottle (cubic expansivity of mercury,=1.8*10"-4) (linear expansivity of glass =8.0*10"-6)
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To calculate the mass of mercury remaining in the bottle, you need to consider the expansion of both the mercury and the glass bottle. Here are the steps to calculate it:
Step 1: Calculate the change in volume of the mercury:
Given the initial mass of mercury (500g) and the mass expelled (2.43g), we can calculate the initial volume of the mercury. Since the density of mercury is approximately 13.6 g/cm^3, we can find the initial volume (V_initial) using the formula: V_initial = mass_initial / density_mercury.
V_initial = 500g / 13.6 g/cm^3 = 36.76 cm^3.
Now, we need to find the change in volume (ΔV) of the mercury due to heating. We can use the formula: ΔV = β_mercury * V_initial * ΔT, where β_mercury is the cubic expansivity of mercury (1.8 * 10^-4) and ΔT is the change in temperature (35°C).
ΔV = (1.8 * 10^-4) * (36.76 cm^3) * (35°C) = 0.229 cm^3.
Step 2: Calculate the change in volume of the glass bottle:
Given the linear expansivity of glass (8.0 * 10^-6) and the initial volume of the glass bottle V_initial, we can calculate the change in volume of the glass (ΔV_glass). We can use the formula: ΔV_glass = α_glass * V_initial * ΔT, where α_glass is the linear expansivity of glass (8.0 * 10^-6) and ΔT is the change in temperature (35°C).
ΔV_glass = (8.0 * 10^-6) * (36.76 cm^3) * (35°C) = 0.010 cm^3.
Step 3: Calculate the final volume of the mercury:
The final volume of the mercury (V_final) can be found by subtracting the change in volume of the mercury (ΔV) and the change in volume of the glass (ΔV_glass) from the initial volume (V_initial).
V_final = V_initial - ΔV - ΔV_glass = 36.76 cm^3 - 0.229 cm^3 - 0.010 cm^3 = 36.521 cm^3.
Step 4: Calculate the mass of the remaining mercury:
Using the density of mercury (13.6 g/cm^3), we can calculate the mass of the remaining mercury (mass_remaining) using the formula: mass_remaining = density_mercury * V_final.
mass_remaining = 13.6 g/cm^3 * 36.521 cm^3 = 496.9356g.
Therefore, the mass of the mercury remaining in the bottle is approximately 496.94g (rounded to two decimal places).
To calculate the mass of the remaining mercury in the bottle, we need to consider the change in volume of both mercury and glass due to heating.
Step 1: Calculate the change in volume of mercury.
The cubic expansivity of mercury (β) is given as 1.8 * 10^(-4) per degree Celsius. We need to convert the temperature change from Celsius to Kelvin since the unit of expansivity is per Kelvin.
ΔV_mercury = (β_mercury * V_mercury * ΔT)
= (1.8 * 10^(-4) * V_mercury * ΔT)
= (1.8 * 10^(-4) * V_mercury * (35 + 273)) [Converting to Kelvin]
Step 2: Calculate the change in volume of glass.
The linear expansivity of glass (α) is given as 8.0 * 10^(-6) per degree Celsius.
Similarly, we need to convert the temperature change from Celsius to Kelvin.
ΔV_glass = (α_glass * V_glass * ΔT)
= (8.0 * 10^(-6) * V_glass * ΔT)
= (8.0 * 10^(-6) * V_glass * (35 + 273)) [Converting to Kelvin]
Step 3: Calculate the total change in volume.
Since glass and mercury are in contact, they experience the same temperature change. Therefore, the total change in volume is the sum of the individual changes:
ΔV_total = ΔV_mercury + ΔV_glass
Step 4: Calculate the remaining mass of mercury.
Since the density (ρ) of mercury is constant, we can use the relationship:
Δm = ρ_mercury * ΔV_total
Now, we can substitute the formulas and given values to calculate the remaining mass of mercury:
Δm = ρ_mercury * (ΔV_mercury + ΔV_glass)
= ρ_mercury * (1.8 * 10^(-4) * V_mercury * (35 + 273) + 8.0 * 10^(-6) * V_glass * (35 + 273))
Finally, subtract the expelled mass (2.43g) from the initial mass (500g) to find the mass of the remaining mercury:
Mass_remaining = Initial_mass - Expelled_mass
= 500g - 2.43g
Please note that you need to provide the values for the initial volume of mercury (V_mercury), the initial volume of the glass (V_glass), and the density of mercury (ρ_mercury) to obtain the specific numerical solution for this problem.