For two cycles coupled in series, the topping cycle has an efficiency of $$30\% $$ and the bottoming cycle has an efficiency of $$20\% $$. The overall combined cycle efficiency is

An iron cube at a temperature of $$400$$ deg $$C$$ is dropped into an insulated bath containing $$10$$ $$kg$$ water at $${25^ \circ }C.$$ The water finally reaches a temperature of $${50^ \circ }C$$ at steady state. Given that the specific heat of water is equal to $$4186$$ $$J/kgK,$$ find the entropy changes for the iron cube and the water. Is the process irreversible ? If so, why?

A steam plant has the boiler efficiency of $$92\% $$, turbine efficiency (mechanical) of $$94\% $$, generator efficiency of $$92\% $$ and cycle efficiency of $$44\% $$. If $$6\% $$ of the generated power is used to run the auxiliaries, the overall plant efficiency is

In a hydroelectric station, water is available at the rate of $$175{m^3}/s$$ under a head of $$18m.$$ The turbines run at a speed of $$150$$ $$rpm$$ with overall efficiency of $$82\% $$. Find the number of turbines required if they have the maximum specific speed of $$460.$$