First slide

Thermal expansion

Question

A glass flask of volume one litre at $0^{0}$ C is filled, level full of mercury at this temperature. The flask and mercury are now heated to l00°C. How much mercury will spill out, if coefficient of volume expansion of mercury is 1 .82 x $10^{- 4} /^{0} C$ and linear expansion of glass is 0.1 x $10^{- 4} /^{0} C$ respectively?

Moderate

A

21.2 cc
B

15.2 cc
C

1.52 cc
D

2.12 cc

Solution

Due to volume expansion of both liquid and vessel, the change in volume of liquid relative to container is given by
${∆V = V}_{0} [γ_{L} - γ_{g}] ∆ θ$
Given $V_{0} = 1000 cc, α_{g} = 0.1 \times 10^{- 4} /^{0} C$
$∴ γ_{g} = 3 α_{g} = 3 \times 0.1 \times 10^{- 4} /^{0} C$ = $0.3 \times 10^{- 4} /^{0} C$
$∆ V = 1000 [1.82 \times 10^{- 4} - 0.3 \times 10^{- 4}] \times 100$
= 15.2 cc

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