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 single stage impulse turbine with rotor diameter of $$2$$ $$m$$ and a speed of $$3000$$ $$rpm$$ when the nozzle angle is $${20^0},$$ the optimum velocity of steam in $$m/s$$

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