A gas contained in a cylinder is compressed, the work required for compression being $$5000$$ $$kJ.$$ During the process, heat interaction of $$200$$ $$kJ$$ causes the surroundings to the heated. The change in internal energy of the gas during the process is

At a hydro electric power plant site, available head and flow rate are $$24.5$$ $$m$$ and $$10.1{m^3}/s$$ respectively. If the turbine to be installed is required to run at $$4.0$$ revolution per second ($$rps$$) with an overall efficiency of $$90\% $$, the suitable type of turbine for this site is _______________.

A centrifugal pump is required to pump water to an open water tank situated $$4$$ $$km$$ away from the location of the pump through a pipe of diameter $$0.2$$ $$m$$ having Darcy’s friction factor of $$0.01.$$ The average speed of water in the pipe is $$2$$ $$m/s.$$ if it is maintain a constant head of $$5$$ $$m$$ in the tank, neglecting other minor losses, the absolute discharge pressure at the pump exist is ______________