A Carnot engine $$(CE$$-$$1)$$ works between two temperature reservoirs $$A$$ and $$B,$$ where $${T_A} = 900K$$ and $${T_B} = 500K.$$ A second Carnot engine $$(CE$$-$$2)$$ works between temperature reservoirs $$B$$ and $$C,$$ where $${T_c} = 300\,\,K.$$ In each cycle of $$CE$$-$$1$$ and $$CE$$-$$2,$$ all the heat rejected by $$CE$$-$$1$$ to reservoir $$B$$ is used by $$CE$$-$$2.$$ For one cycle operation, if the net $$Q$$ absorbed by $$CE$$-$$1$$ from reservoir $$A$$ is $$150$$ $$MJ,$$ the net heat rejected to reservoir $$C$$ by $$CE$$-$$2$$ (in $$MJ$$) is ______________

A reversed Carnot cycle refrigerator maintains a temperature of $$ - {5^ \circ }C.$$ The ambient air temperature is $${35^ \circ }C.$$ The heat gained by the refrigerator at a continuous rate is $$2.5$$$$kJ/s.$$ The power (in watt) required to pump this heat out continuously is _____________.

The following four figures have been drawn to represent a fictitious thermodynamic cycle, on the $$P$$-$$v$$ and $$T$$-$$S$$ plates

According to the first law of thermodynamics, equal areas are enclosed by

An industrial heat pump operates between the temperatures of $${27^ \circ }C$$ and $$ - {13^ \circ }C.$$ The rates of heat addition and heat rejection are $$750$$ $$W$$ and $$1000$$ $$W,$$ respectively. The $$COP$$ for the heat pump is