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In a vertical U-tube containing a luquid...

In a vertical `U`-tube containing a luquid, the two arms are maintained at different temperatures, `t_(1)` and `t_(2)` . The liquid coplumns in the two arms have heights `l_(1)` and `l_(2)` respectively. The coefficient of volume expansion of the liquid is equal to

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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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