Any thermodynamic cycle operating between two temperature limits is reversible if the product of efficiency when operating as a heat engine and the coefficient of performance when operating as a refrigeration is equal to $$1.$$

A $$1500$$ $$W$$ electrical heater is used to heat $$20$$ $$kg$$ of water $$\left( {{C_p} = 4186\,\,J/kg\,\,K} \right)$$ in an insulated bucket, from a temperature of $${30^{^0}}C$$ to $${80^{^0}}C$$. If the heater temperature is only infinitesimally larger than the water temperature during the process, the change in entropy for the heater is ________$$J/K$$ and for water _______$$J/K.$$

The slopes of constant volume and constant pressure lines in the $$T$$-$$s$$ diagram are ___________ and ___________respectively.

For a given set of operating pressure limits of a Rankine cycle, the highest efficiency occurs for