When 82g of a liquid at 10 degree celsius in a specific gravity bottle...
Calculation of Coefficient of Apparent Expansion of Liquid
In this problem, we are given that 82g of a liquid at 10 degrees Celsius in a specific gravity bottle is heated to 85 degrees Celsius, resulting in the expulsion of 2g of liquid. We need to find the coefficient of apparent expansion of the liquid.
Step 1: Calculate the initial volume of the liquid:
Given that the specific gravity bottle weighs 82g when filled with the liquid at 10 degrees Celsius. Let the density of the liquid be ρ and the volume of the liquid be V.
So, initial mass of the liquid = 82g
Using the formula, mass = density x volume, we have:
82g = ρ x V
V = 82g / ρ
Step 2: Calculate the final volume of the liquid:
When the liquid is heated to 85 degrees Celsius, 2g of liquid is expelled. Let the final volume of the liquid be V'.
So, final mass of the liquid = 82g - 2g = 80g
Using the formula, mass = density x volume, we have:
80g = ρ x V'
V' = 80g / ρ
Step 3: Calculate the apparent expansion of the liquid:
The apparent expansion of the liquid can be calculated using the formula:
Coefficient of apparent expansion (α) = (V' - V) / (V x (Tf - Ti))
Where Tf = final temperature = 85 degrees Celsius
Ti = initial temperature = 10 degrees Celsius
Step 4: Substitute the values and calculate:
Substitute the values of V, V', Tf, Ti into the formula for the coefficient of apparent expansion and calculate the value of α.
Step 5: Interpret the result:
The value obtained for the coefficient of apparent expansion of the liquid represents how much the volume of the liquid expands per degree Celsius increase in temperature.
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