A glass bottle full at mercury at 0°C has a mass of 500g On being heated through 350°C, 2.43g of mercury is expelled Calculate the mass of mercury remaining in the bottle. Take cubic expansivity of mercury to be 1.8X10-4/K and the linear expansivity of glass to be 8.0x10.6/k
500 - 2.43 = 497.57
To calculate the mass of mercury remaining in the bottle after being heated, we need to consider the change in volume of both the mercury and the glass.
1. Calculate the change in volume of the mercury:
- The initial volume of the mercury can be calculated using its density. The density of mercury at 0°C is approximately 13.6 g/cm³.
- The mass of the mercury is 500g, so its initial volume is given by volume = mass / density = 500g / 13.6 g/cm³.
- Convert the initial volume to cubic meters to match the units of linear expansivity: initial volume = initial volume * (1 cm / 100 m)³.
2. Calculate the change in volume of the glass:
- The linear expansivity of the glass is given as 8.0x10⁻⁶/K.
- The change in length of the glass can be calculated using the formula: ΔL = αLΔT, where ΔL is the change in length, α is the linear expansivity, L is the initial length, and ΔT is the change in temperature.
- Since the glass bottle is cylindrical, and its volume is given by V = πr²L, where r is the radius and L is the length, we can substitute in the expression for L from the previous step.
- Differentiate the volume equation with respect to r to find the change in volume due to the change in length.
3. Calculate the mass of the expelled mercury:
- The mass of the expelled mercury is given as 2.43g.
4. Calculate the remaining mass of the mercury:
- The remaining mass of the mercury can be calculated by subtracting the mass of the expelled mercury from the initial mass of the mercury.
Please note that the provided value for the linear expansivity of glass (8.0x10⁻⁶/K) is likely a typo, as it is extremely small. The correct value should be used in the calculations.
To find the mass of mercury remaining in the bottle after being heated, we need to consider the changes in volume of both the glass bottle and the mercury due to the temperature increase.
Let's break down the problem step by step:
Step 1: Calculate the volume of mercury expelled.
First, we need to find the initial volume of mercury in the bottle. We can use the density of mercury to relate its mass to its volume.
Density of mercury = 13.6 g/cm^3
Given that the mass of mercury expelled is 2.43 g, we can use the formula: Density = Mass / Volume, to find the volume as follows:
Volume of expelled mercury = Mass of expelled mercury / Density = 2.43 g / 13.6 g/cm^3
Convert the mass to grams: 2.43 g
Step 2: Calculate the change in volume of the glass bottle.
Using the linear expansivity of glass, we can calculate the change in length (ΔL) of the glass bottle due to the temperature increase.
Given: linear expansivity of glass (α) = 8.0 x 10^-6 /K,
Change in temperature (ΔT) = 350°C.
The formula for change in length is: ΔL = αL₀ΔT,
where L₀ is the initial length of the glass bottle.
Step 3: Calculate the change in volume of the glass bottle.
The change in volume of the glass bottle can be determined using the formula: ΔV = 3ΔL₀, where ΔL₀ is the initial length of the glass bottle.
Step 4: Calculate the final volume of the mercury.
The final volume of the mercury can be found by subtracting the change in volume of the glass bottle from the initial volume of mercury:
Final volume of mercury = Initial volume of mercury - Change in volume of the glass bottle
Step 5: Calculate the mass of the remaining mercury.
Finally, using the density of mercury, we can calculate the mass of the remaining mercury.
Mass of remaining mercury = Final volume of mercury x Density of mercury
Note: Since the problem does not specify the initial volume of mercury in the bottle, we cannot determine the exact mass of mercury remaining. However, we can calculate the mass change based on the given information.