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$EXAMPLE 11.5Calculate the entropy change when 1.0 \mathrm{~kg} ice at 0^{\circ} \mathrm{C} melts into water at 0^{\circ} \mathrm{C} . Latent heat of fusion of ice L_{f}=3.36 \times 10^{5} \mathrm{~J} \mathrm{~kg}^{-1} .$  $Show that ratio of the root mean square speeds of molecules of two different gases at a certain temperature is equal to the square root of the inverse ratio of their masses.$  $Which one of the following process is irreversible?(a) Slow compressions of an elastic spring.(b) Slow evaporation of a substance in an isolated vessel.(c) Slow compression of a gas.(d) A chemical explosion.$  $EXAMPLE 11.4The turbine in a steam power plant takes steam from a boiler at 427{ }^{\circ} \mathrm{C} and exhausts into a low temperature reservoir at 77^{\circ} \mathrm{C} . What is the maximum possible efficiency.$  $A carnot engine utilises an ideal gas. The source temperature is 227^{\circ} \mathrm{C} and the sink temperature is 127^{\circ} \mathrm{C} . Find the efficiency of the engine. Also find the heat input from the source and heat rejected to the sink when 10000 \mathrm{~J} of work is done.$  $A heat engine performs 100 \mathrm{~J} of work and at the same time rejects 400 \mathrm{~J} of heat energy to the cold reservoirs. What is the efficiency of the engine?$  $Is it possible to convert internal energy into mechanical energy? Explain with an example.$  