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A thin walled cylindrical metal vessel of linear coefficient of expansion $10^{-3} $ $^o C^{-1}$ contains benzenr of volume expansion coefficient $10^{-3}$ $^o C^{-1}$. If the vessel and its contents are now heated by $10^o C,$ the pressure due to the liquid at the bottom.
increases by $2\%$
decreases by $1\%$
decreases by $2\%$
remains unchanged
Solution
$\gamma_{\text {vessel}}=3 \alpha_{\text {vessel}}=3 \times 10^{-3}$
$\gamma_ {liquid}$ $=10^{-3}$
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\left(\gamma_{\text {vexsel }}-\gamma_{\text {liguid}}\right) \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 $2 \%$
