a wieghtthermometer contains 200 g of mercury at 0 degree centigrade is surrounded by a liquid in a bath and 8 g of mercury flows out . what was the temperature of the bath if co-eff of apparent expansion of mercury is 0.00018 ?

Dear Student,

Please find below the solution to the asked query:

Initial volume of the mercury is 200 g, then the mass flowing out, when the temperature increases is 8 g. Therefore, the 

The relation between the mass and the density of the thermometer is $m=V\rho \Rightarrow m\propto \rho$

So, along with the temperature the mass and density varies in the same manner. So, the relation for the mass flown out is,

$$\begin{gathered} ∆\rho =\rho \left(3\alpha \right)\left(∆T\right)\Rightarrow ∆m=m\left(3\alpha \right)\left(∆T\right) \\ \Rightarrow 8=200\times \left(3\times 0.00018\right)\times \left(T-0\right)\Rightarrow 8=6\times 0.018\times T \\ \Rightarrow T=\frac{2000}{27}=74.07{ }^{0}C \end{gathered}$$



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