Question

A mercury thermometer is used to measure within temperature range $0-{100}^{\circ }C$. Internal diameter of the glass tube is $0.4mm$ and the distance between $0^{\circ }C$ and ${100}^{\circ }C$ points is $21cm$ . The coefficient of volume expansion of mercury is $0.0002{/}^{\circ }C$. and the coefficient of linear expansion of glass is $0.000008{/}^{\circ }C$ . Assume that temperature variation takes place only of the bulb portion and temperature of the mercury inside remains homogenous. The internal volume of the bulb at $0^{\circ }C$ is

• A. $2.5c{m}^3$
• B. $3.0c{m}^3$
• C. $1.5c{m}^3$
• D. $15c{m}^3$

Answer 1

The correct option is C $1.5c{m}^3$

Given: $Y_m=0.0002{/}^{\circ }C,{\alpha }_g=0.000008{/}^{\circ }C,\Delta T={100}^{\circ }C,r=0.2mm,l=21cm{Y}_g=3{\alpha }_g=3\times 0.000008=0.000024{/}^{\circ }C$

Volume of the mercury in tube at ${100}^{\circ }C=$ Volume of mercury overflown from the bulb.

$\left(\pi r^2\right)l=V_0(Y_m-Y_g)\Delta T$

$V_0=\frac{\pi \times {0.02}^2\times 21}{(0.0002-0.000024)\times 100}$

$V_0=\frac{22}{7}\times \frac{4}{176}\times 21=1.5c{m}^3$
Final answer (a)