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A U-tube has a liquid of density rho(0) ...

A U-tube has a liquid of density `rho_(0)` at `0^(@) C`. In the two limbs they are kept to a length `l_(1)` and `l_(2)` at a constant temperature of `t_(1)` and `t_(2)` respectively. Then, the cubical expansion coefficient will be

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Pressure at the bottom of two limbs
`P_(o)+h_(1)rho_(1)g=P_(0)+h_(2)rho_(2)g`
or `(h_(1))/(h_(2))=(rho_(2))/(rho_(1))`…………..(1)
Now `rhio_(1)=rho_(o)//(1+gamma_(r)t_(1))`
`rho_(2)=rho_(0)//(1+tgamma)t_(2))`
or `(rho_(2))/(rho_(1))=(1+gamma_(r)t_(1))/(1+gamma_(r)t_(2))`.............2
solving `gamma_(r)=(h_(2)-h_(1))/(h_(1)t_(2)-h_(2)t_(1))`
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