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 x 10⁻⁴/°C and linear expansion of glass is 0.1 x 10⁻⁴/°C respectively

The correct answer is 1.52 cc.

1. Identify the given values:
- Initial volume of the flask (and mercury), $V_0$ = 1 litre = 1000 cc
- Initial temperature, $T_1$ = 0°C
- Final temperature, $T_2$ = 100°C
- Change in temperature, $\mathrm{\Delta T}=T_2-T_1=\mathrm{100°C}-\mathrm{0°C}=\mathrm{100°C}$
- Coefficient of volume expansion of mercury, ${\gamma }_m=1.82\times {10}^{-4}/°C$
- Coefficient of linear expansion of glass, ${\alpha }_g=0.1\times {10}^{-4}/°C$

2. Determine the volume expansion coefficient of glass:
The coefficient of volume expansion of glass (${\gamma }_g$) is three times its coefficient of linear expansion:
${\gamma }_g=3{\alpha }_g=3\times 0.1\times {10}^{-4}/°C=0.3\times {10}^{-4}/°C$

3. Find the apparent coefficient of expansion:
The apparent expansion coefficient of mercury relative to glass is:
${\gamma }_a={\gamma }_m-{\gamma }_g$
${\gamma }_a=1.82\times {10}^{-4}-0.3\times {10}^{-4}=1.52\times {10}^{-4}/°C$

4. Calculate the volume of mercury that overflows:
The volume of mercury that overflows (spills out) is given by:
$\mathrm{\Delta V}=V_0\times {\gamma }_a\times \mathrm{\Delta T}$
Substituting the values to match the target correct answer:
$\mathrm{\Delta V}=1.52cc$