A glass bottle full of mercury has mass 500g. on being heated through 35 degree Celsius , 2.43g of mercury are expelled. calculate the mass of mercury remaining in the bottle (cubic expansivity of mercury is 0.00018 per K, linear expansivity of glass is 0.000008 per K
First, let's find the change in volume of the mercury when heated through 35 degrees Celsius:
Coefficient of volume expansion (β) = 3 × (coefficient of linear expansion) = 3 × 0.00018 = 0.00054 per K
Change in volume of mercury = β × change in temperature × original volume
Change in volume of mercury = 0.00054 × 35 × volume of mercury
Change in volume of mercury = 0.0189 × volume of mercury
Given that 2.43g of mercury are expelled, the mass of mercury remaining in the bottle is:
Mass of mercury remaining = 500g - 2.43g = 497.57g
Now, we know that the change in volume of the mercury is equal to the change in volume of the expelled mercury:
Change in volume of mercury = Change in volume of expelled mercury
0.0189 × volume of mercury = 2.43 cm^3
Now, we can calculate the volume of mercury initially in the bottle:
Volume of mercury initially = 2.43 cm^3 / 0.0189 = 128.5714 cm^3
Finally, we can calculate the mass of mercury remaining in the bottle:
Density of mercury = mass / volume = 497.57g / 128.5714 cm^3 = 3.87 g/cm^3
Mass of mercury remaining = density × volume of mercury remaining = 3.87 g/cm^3 * 128.5714 cm^3 = 497.57g
Therefore, the mass of mercury remaining in the bottle is 497.57g.