Q22 of 64 Page 12

The volume of a glass vessel is 1000 cc at 20°C. What volume of mercury should be poured into it at this temperature so that the volume of the remaining space does not change with temperature? Coefficients of cubical expansion of mercury and glass are 1.8 × 10–4 °C–1 and 9.0 × 10–6 °C–1 respectively.


Given:
Volume of Glass vessel at T1 = 20 ° C is : Vg = 1000 cc.

Coefficients of cubical expansion of mercury: γHg =1.8 ×10–4 °C–1.


Coefficients of cubical expansion of Glass : γg = 9.0 × 10–6 °C–1.


Now Let the Volume of mercury at T1 = 20° C be VHg. We need to find VHg.


Due to Change in temperature, Volume Expansion takes place.


When mercury is added in the glass, it consumes some amount of volume VHg, thus the remaining space is Vg - VHg. ----( Initial).


When volume expansion takes place the changed volume of glass and mercury inside it is V’g and V’Hg respectively. Thus the remaining space after the volume expansion is V’g –V’Hg.--( Final)


The given condition says that the remaining space should not change with temperature which means: Initial = Final



Formula used :
 Where V’ is the changed volume at T2 and V is the initial volume at T1.


For Glass: V’g = Vg( 1 + γgΔT)


For Mercury : V’Hg = VHg( 1 + γHgΔ T)


Substituting we get,










Hence, the volume of mercury poured into the glass it at 20 ° C so that the volume of the remaining space does not change with temperature is 50 cc.


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 21

A glass window is to be fit in an aluminium frame. The temperature on the working day is 40°C and the glass window measures exactly 20 cm × 30 cm. What should be the size of the aluminium frame so that there is no stress on the glass in winter even if the temperature drops to 0°C? Coefficients of linear expansion for glass and aluminium are 9.0 × 10–6 °C–1 & 24×10–6°C–1respectively.

 23

An aluminium can of cylindrical shape contains 500 cm3 of water. The area of the inner cross section of the can is 125 cm2. All measurements refer to 10°C. Find the rise in the water level if the temperature increases to 80°C. The coefficient of linear expansion of aluminium = 23 × 10–6 °C–1 and the average coefficient of volume expansion of water = 3.2 × 10–4 °C–1 respectively.

 24

A glass vessel measures exactly 10 cm × 10 cm × 10 cm at 0°C. It is filled completely with mercury at this temperature. When the temperature is raised to 10°C, 1.6 cm3 of mercury overflows. Calculate the coefficient of volume expansion of mercury. Coefficient of linear expansion of glass = 6.5 × 10–6 °C–1.