A glass vessel with a capacity of 200 ml is completely filled with turpentine at 5 °C. The cubic expansion coefficient of glass is 24 x 10-6/°C. The vessel and turpentine are heated to 80 °C. If the apparent expansion coefficient of turpentine is 90×10-6/°C, calculate the absolute expansion coefficient of turpentine.
First, we need to calculate the total volume increase of the system when heated from 5°C to 80°C.
The total volume increase can be calculated using the formula:
ΔV = V * β_v * ΔT
Where:
ΔV = Total volume increase
V = Initial volume of the system (glass vessel + turpentine) = 200 ml
β_v = Cubic expansion coefficient of glass = 24 x 10^-6/°C
ΔT = Change in temperature = 80°C - 5°C = 75°C
ΔV = 200 * 24 x 10^-6/°C * 75°C
ΔV = 200 * 0.000024 * 75 = 0.36 ml
Now, let's calculate the volume increase due to the expansion of turpentine alone:
The volume of turpentine initially was 200 ml. Therefore,
Turpentine final volume = Initial volume + Volume increase
Turpentine final volume = 200 ml + 0.36 ml = 200.36 ml
Now, let's calculate the volume increase of turpentine alone:
ΔV_turpentine = 200 * 90 x 10^-6/°C * 75°C
ΔV_turpentine = 200 * 0.00009 * 75 = 1.35 ml
Finally, let's calculate the absolute expansion coefficient of turpentine:
Absolute expansion coefficient = ΔV_turpentine / (V * ΔT)
Absolute expansion coefficient = 1.35 ml / (200 ml * 75)
Absolute expansion coefficient = 0.00000675 / °C
Therefore, the absolute expansion coefficient of turpentine is 6.75 x 10^-6/°C.