Answer:
Decrease in level by thermal contraction = 0.0076 mm
Drops in level = 3 mm
Therefore The decrease in level is not due to thermal contraction
Explanation:
From linear expansivity,
L₂ = L₁ +(1 + αΔT).............................. equation 1
Where L₂ = final length (m), L₁ = initial length, α = linear expansivity of liquid, ΔT = change in temperature.
Where L₁ = level of coffee in the glass cup = V/(πd²)/4..................... equation 2
L₁ = 4V/πd², where V= Volume of coffee, d = diameter of the cup,
L₁ = 350cm³, d = 7.00cm, and π = 22/7 = 3.143
applying these values in equation 2 above,
∴ L ₁=( 4×350)/(3.143×7²)
L₁ = 9.09
α = γ/3 Where γ = Volumetric expansion coefficient of liquid. = 0.00005/°C
α = 0.00005/3 = 0.0000167/°C, ΔT = L₂ - L₁ = 45 -95 = -50 °C.
Applying these values in equation 1 above,
L₂ = 9.09 [1+{0.0000167×(-50)}]
L₂ = 9.09 [1 - 0.000833]
L₂ = 9.09(0.999167)
L₂ = 9.082cm
∴ ΔL = Decrease in length = L₂ - L₁ = 9.082 - 9.09 = 0.3 cm
ΔL = 0.0076
Decrease in level =0.076 mm
From the above, the decrease in level is not due to thermal contraction.
As Thermal contraction is less than Drops in level.
