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(a) A steel tank has internal volume `V_0` (= 100 litre). It contains half water ( volume = `(V_0)/2` ) and half kerosene oil at temperature `theta_(1) = 10^(@)C` Calculate the mass of kerosene that flows out of the tank at temperature of `theta_(2)=40^(@)C`. Coefficient of cubical expansion for different substances are: `gamma_(k)=10^(-3).^(@)C^(-1), gamma_(w)=2xx10^(-4) .^(@)C^(-1), gamma_("steel")=1.2xx10^(-5).^(@)C^(-1)`. density of kerosene at `10^(@)C` is `rho_(1)=0.8 kg` /litre. (b) In the last problem the height of water in the container at `theta_(1)=10^(@)C` is `H_1 = 1.0 m`. Find the height of water at `theta_(2) = 40^(@)C`.

Answer» Correct Answer - `(a) Delta m =(V_(0) rho_(1))/2 ((gamma_(k)+gamma_(w)-2gamma_(s)))/((1+gamma_(k) Delta theta)) Delta theta`; =1.37 kg [where `Delta theta=theta_(2) -theta_(1)`]
(b) `(H_(1)[1+gamma_(w)Delta theta])/([1+2/3gamma_(s)Delta theta]) =1.0057 m`


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