A rigid closed vertical cylindrical vessel of 15 cm diameter contains 5 kg water at $80^{\circ} \mathrm{C}$ with $10 \%$ quality. The water is heated till its temperature reaches $130^{\circ} \mathrm{C}$. Considering only a horizontal separated interface between liquid and vapor, the dip in the liquid level after the heating process is $\_\_\_\_$ cm (rounded off to 2 decimal places).

Properties of water at various saturation temperatures are given in the table below.

Temperature	Specific volume		Specific internal energy
$$ \left(\mathrm{T}^{\circ} \mathrm{C}\right) $$	$$ v_f\left(\mathrm{~m}^3 / \mathrm{kg}\right) $$	$$ v_g\left(\mathrm{~m}^3 / \mathrm{kg}\right) $$	$$ u_f(\mathrm{~kJ} / \mathrm{kg}) $$	$$ u_g(\mathrm{~kJ} / \mathrm{kg}) $$
80	0.001029	3.4053	334.97	2481.60
130	0.001070	0.66808	546.10	2539.50

T, $v$ and $u$ ae temperatue, specific golume, and specific internal energy, respectively. subscripts $f$ and $g$ represent saturated liquid and saturated vapor, respectively.

In Fe-Fe₃C phase diagram, the eutectoid composition is 0.8 weight % of carbon at 725 ºC. The maximum solubility of carbon in α-ferrite phase is 0.025 weight % of carbon. A steel sample, having no other alloying element except 0.5 weight % of carbon, is slowly cooled from 1000 ºC to room temperature. The fraction of pro-eutectoid α-ferrite in the above steel sample at room temperature is

Steam enters a turbine at $$30bar,$$ $${300^ \circ }C$$ $$\left( {u = 2750\,\,kJ/kg,\,\,h = 2993\,\,kJ/kg} \right)$$ and exits the turbine as saturated liquid at $$15$$ $$kPa$$ $$\left( {u = 225\,\,kJ/kg,\,\,h = 226\,\,kJ/kg} \right)$$.
Heat loss to the surrounding is $$50$$ $$kJ/kg$$ of steam flowing through the turbine. Neglecting changes in kinetic energy and potential energy, the work output of the turbine (in $$kJ/kg$$ of steam) is _____________

In the figure shown, the system is a pure substance kept in a piston- cylinder arrangement. The system is initially a two- phase mixture containing $$1$$ $$kg$$ of liquid and $$0.03$$ $$kg$$ of vapour at a pressure of $$100kPa.$$ Initially, the piston rests on a set of stops, as shown in the figure. A pressure of $$200kPa$$ is required to exactly balance the weight of the piston and the outside atmospheric pressure. Heat transfer takes place into the system until its volume increases by $$50\% $$. Heat transfer to the system occurs in such a manner that the piston, when allowed to move, does so in a very slow (quasi-static / quasi-equilibrium) process. The thermal reservoir from which heat is transferred to the system as a temperature of $${400^ \circ }C$$. Average temperature of the system boundary can be taken as $${175^ \circ }C.$$ Heat transfer to the system is $$1kJ$$, during which its entropy increases by $$10$$ $$J/K.$$

Specific volume of liquid $$\left( {{v_f}} \right)$$ and vapour $$\left( {{v_g}} \right)$$ phases, as well as values of saturation temperatures, are given in the table below.

The net entropy generation (considering the system and the thermal reservoir together) during the process is closest to