In a steady state steady flow process taking place in a device with a single inlet and a single outlet, the work done per unit mass flow rate is given by $$W = - \int_{inlet}^{outlet} {vdp} ,$$ where $$v$$ is the specific volume and $$P$$ is the pressure. The expression for $$'W'$$ given above

$$2$$ moles of oxygen are mixed adiabatically with another $$2$$ moles of oxygen in mixing chamber, so that the final total pressure and temperature of the mixture become same as those of the individual constituents at, their initial states. The universal gas constant is given as $$R$$. The change in entropy due to mixing, per mole of oxygen, is given by

$$A$$ gas expands in a frictionless piston-cylinder arrangement. The expansion process is very slow, and is resisted by an ambient pressure of $$100kPa.$$ During the expansion process, the pressure of the system (gas) remains constant at $$300$$ $$kPa.$$ The change in volume of the gas is $$0.01{m^3}.$$

The maximum amount of work that could be utilized from the above process 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