The mercury will rise 4.5 cm in the capillary tube.
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This problem is about Density.
Density is the ratio of mass to the volume of the object.
[tex]\large {\boxed {\rho = \frac{ m }{ V } } }[/tex]
ρ = density of object ( kg / m³ )
m = mass of object ( kg )
V = volume of object ( m³ )
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The volume expansion of object could be calculated using this following formula.
[tex]\boxed {V = Vo ( 1 + 3 \alpha \Delta t )}[/tex]
where:
V = final volume after expansion ( m³ )
Vo = initial volume before expansion ( m³ )
α = coefficient of expansion ( /K )
Δt = change in temperature ( K )
Let's tackle the problem!
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Given:
initial volume = Vo = 0.100 cm³
cross-sectional area = A = 0.012 mm² = 0.012 × 10⁻² cm²
coefficient of volume expansion of mercury = γ = 1.8 × 10⁻⁴ /K
change in temperature = Δt = 35 - 5 = 30°C
Asked:
the rise of mercury column = h = ?
Solution:
[tex]h = \Delta V \div A[/tex]
[tex]h = (V_o \gamma \Delta t) \div A[/tex]
[tex]h = (0.100 \times 1.8 \times 10^{-4} \times 30) \div (0.012 \times 10^{-2})[/tex]
[tex]h = 4.5 \texttt{ cm}[/tex]
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Grade: High School
Subject: Physics
Chapter: Expansion
