Question

A thin walled cylindrical metal vessel of linear coefficient of expansion ${10}^{-3}{}^{\circ }{C}^{-1}$ contains benzene of volume expansion coefficient ${10}^{-3}{}^{\circ }{C}^{-1}$. If the vessel and its contents are now heated by ${10}^{\circ }C$, the pressure due to the liquid at the bottom

• A. increases by $2\%$
• B. decreases by $1\%$
• C. decreases by $2\%$
• D. remains unchanged

Answer 1

Answer: (C)

decreases by $2\%$

${\gamma }_{vessel}=3{\alpha }_{vessel}=3\times {10}^{-3}$
${\gamma }_{liquid}={10}^{-3}$
When the liquid is heated, the level of liquid falls which will result in decrease of pressure.
Change in volume of liquid: $\Delta V=V({\gamma }_{vessel}-{\gamma }_{liquid})\times \Delta T=V\times 2\times {10}^{-3}\times (10-0)=0.02$
$\therefore \frac{\Delta V}{V}=0.02$
$\Rightarrow \frac{\Delta h}{h}=0.02$
$\Rightarrow$ decrease in pressure is $0.02\times 100\%=2\%$
Hence, decrease in pressure at bottom of the vessel is $2\%$.