Q$.2$ Short Questions $($each question carries $3$ marks$)$

$(15$ marks$)$

a$)$ Two reversible heat pumps $($in heating mode$)$ operate in series between a hot water storage tank at $60C$ and a low$-$temperature reservoir at $12C.$ The two engines have equal energy efficiencies. Assume that each reversed heat engine operates on the Carnot Cycle. Calculate the fluid temperature between the two engines at which heat is supplied to the second engine.

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b$)$ The specific entropy of wet steam at $10$ bar is $3\mathrm{.}66k\frac{J}{k}g.K.$ Determine its dryness fraction. $($You may refer to the below values for saturated water$/$steam$)$

$\backslash$table$[[$Pressure $($bar$),s_f(k\frac{J}{k}gK),s_{fg}(k\frac{J}{k}gK),s_g(k\frac{J}{k}gK)$