A vertical cylinder with a freely floating piston contains $$0.1$$ $$kg$$ air at $$1.2$$ bar and a small electrical resistor. The resistor is wired to an external $$12$$ Volt battery. When a current of $$1.5$$ amps is passed through the resistor for $$90$$ $$secs,$$ the piston sweeps a volume of $$0.01$$ $${m^3}.$$ Assume $$(i)$$ piston and the cylinder are insulated and $$(ii)$$ air behaves as a ideal gas with $${C_v} = 700\,\,J/kg\,K.$$
Find the rise in temperature of air.

Figure below shows a reversible heat engine $${E_R}$$ having heat interactions with three constant temperature systems. Calculate the thermal efficiency of the heat engine.

The equivalent evaporation $$(kg/hr)$$ of a boiler producing $$2000$$ $$kg/hr$$ of steam with enthalpy content of $$2426$$ $$kJ/kg$$ from feed water at temperature $${40^ \circ }C$$ (liquid enthalpy $$=168$$ $$kJ/kg$$) is (Enthalpy of vaporization of water at $${100^0}C = 2258$$ $$kJ/kg$$).

When a system executes an irreversible cycle: