Water (density $$ = 1000$$ $$kg/{m^3}$$) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of $$1$$ $$kg/s.$$ If the pressure drop across the pipe is $$100$$ $$kPa,$$ the minimum power required to pump the water across the pipe, in watts, is

One $$kg$$ of an ideal gas (gas constant, $$R = 400$$ $$J/kg.K;$$ specific heat at constant volume, $${c_v} = 1000\,J/kg.K$$ at $$1$$ bar, and $$300$$ $$K$$ is contained in a sealed rigid cylinder. During an adiabatic process, $$100$$ $$kJ$$ of work is done on the system by a stirrer. The increase in entropy of the system is _________ $$J/K.$$

A heat pump absorbs $$10$$ $$kW$$ of heat from outside environment at $$250$$ $$K$$ while absorbing $$15$$ $$kW$$ of work. It delivers the heat to a room that must be kept warm at $$300$$ $$K.$$ The Coefficient of performance $$(COP)$$ of the heat pump is _____________.

Which one of the following is NOT a rotating machine?