A glass flask of volume one litre at 0° C is filled, level full of mercury at this temperature. The flask and mercury are now heated to 100° C. How much mercury will spill out, if coefficient of volume expansion of mercury is 1.82 × 10-4 / ° C and linear expansion of glass is 0.1 × 10-4 / ° C respectively?

Question

A glass flask of volume one litre at 0° C is filled, level full of mercury at this temperature. The flask and mercury are now heated to 100° C. How much mercury will spill out, if coefficient of volume expansion of mercury is 1.82 × 10-4 / ° C and linear expansion of glass is 0.1 × 10-4 / ° C respectively? (A) 21.2 cc (B) 15.2 cc (C) 1.52 cc (D) 2.12 cc

Tardigrade Admin · Accepted Answer

Due to volume expansion of both liquid and vessel, the change in volume of liquid relative to container is given by

Δ V = V_{0} [γ_{L} - γ_{g}] Δ θ

Given

V_{0} = 1000 cc, α_{g} = 0.1 \times 1 0^{- 4} /^{\circ} C

∴ γ_{g} = 3 α_{g} = 3 \times 0.1 \times 1 0^{- 4} /^{\circ} C

= 0.3 \times 1 0^{- 4} /^{\circ} C

∴ Δ V = 1000 [1.82 \times 1 0^{- 4} - 0.3 \times 1 0^{- 4}] \times 100

= 15.2 cc

21.2 cc

15.2 cc

1.52 cc

2.12 cc

Due to volume expansion of both liquid and vessel, the change in volume of liquid relative to container is given by ΔV=V0​[γL​−γg​]Δθ Given V0​=1000cc,αg​=0.1×10−4/∘C ∴γg​=3αg​=3×0.1×10−4/∘C =0.3×10−4/∘C ∴ΔV=1000[1.82×10−4−0.3×10−4]×100 =15.2cc