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 _______________

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 _______________________.