The coefficient of volumetric expansion of mercury is 8×10−5∘C. A thermometer bulb has a volume 10−6m3 and cross section of stem is 0.004cm2. Assuming that bulb is filled with mercury at 0∘C, then the length of the mercury column at 100∘C is:
4.5 cm
The volumetric expansion can be written as,
V2=V1(1+γΔθ)
where, V2 is the final volume, V1 is the initial volume, γ is the coefficient of volumetric expansion and Δθ is the change in temperature.
or, Change in volume,V2−V1=V1γΔθ
As we know, Change in volume=Area×Change in length
or, V2−V1=Area×Change in length
or, Change in length=V2−V1Area
or, Change in length=V1γΔθA
Given, V1=10−6 m3, A=0.004 cm2=0.004×10−4 m2, γ=8×10−5 ∘C,
Δθ=100−0=100∘C
Therefore,
Change in length=10−6×8×10−5×1000.004×10−4
or, Change in length=2×10−2m=2cm