An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript $$1$$) and at the end (subscript $$2$$) of the process with usual notation are:
$${P_1} = 100\,\,kPa,\,\,{V_1} = 0.2\,{m^3}$$ and $${P_2} = 200\,\,kPa,\,\,{V_2} = 0.1\,{m^3}$$
and the gas constant, $$R = 0.275$$ $$kJ/kg$$-$$K.$$ The magnitude of the work required for the process (in $$kJ$$) is _______________

The INCORRECT statement about regeneration in vapor power cycle is that

In a steam power plant operating on an ideal Rankine cycle, super-heated steam enters the turbine at $$3$$ $$MPa$$ and $${350^ \circ }C.$$ The condenser pressure is $$75$$ $$kPa.$$ Thermal efficiency of the cycle is ___________ percent.

Given data:

For saturated liquid, at $$P=75$$ $$kPa,$$
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,{h_f} = 384.39\,\,kJ/kg, \cr & \,\,\,\,\,\,\,\,\,\,{v_f} = 0.001037\,\,{m^3}/kg, \cr & \,\,\,\,\,\,\,\,\,\,{s_f} = 1.213\,\,kJ/kg K \cr} $$

At $$75$$ $$kPa,$$ $${h_{fg}} = 2278.6\,\,kJ/kg,$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,{s_{fg}} = 6.2434\,\,kJ/kg$$-$$K$$

At $$P=3$$ $$MPa$$ and
$$\,\,\,\,\,\,\,\,\,\,T = {350^ \circ }C\,\,\,$$ (Superheated steam),
$$\,\,\,\,\,\,\,\,\,\,h = 3115.3\,\,kJ/kg,$$
$$\,\,\,\,\,\,\,\,\,\,s = 6.7428\,\,kJ/kg$$-$$K$$

Consider two hydraulic turbines having identical specific speed and effective head at the inlet. If the speed ratio $$\left( {{{{N_1}} \over {{N_2}}}} \right)$$ of the two turbines is $$2,$$ then the respective power ratio $$\left( {{{{P_1}} \over {{P_2}}}} \right)$$ is _______________________.