Compare the ideal Rankine cycle to the Carnot cycle how does

Compare the ideal Rankine cycle to the Carnot cycle, how does their thermal efficiency compare? What are some shortcomings of each model? What effect does increasing the boiler pressure of an ideal Rankine cycle have on thermal efficiency? What effect does increasing the average temperature at which energy is transferred by heal transfer to an ideal Rankine cycle have on thermal efficiency? What happens to thermal efficiency if the temperature of energy rejected increases? The ideal Brayton and Rankine cycles are composed of the same four processes, yet look different when represented on a T-s diagram. Explain. What changes would you expect to see in the conservation of momentum equation, for a traveling wave, when considering a stationary observer and an observer on the wave? Can the coefficient of performance of a heat pump have a value less than one? If the heat exchanger is omitted from the system of Fig. 7, what is the effect on the coefficient of performance? If your car\'s air conditioner discharges only warm air while operating, what might be wrong with it?

Solution

A)

CARNOT CYCLE

Heat addition is done by keeping temperature constant.

Heat rejection is done by keeping temperature constant.

RANKINE CYCLE

Heat addition is done by keeping pressure constant.

Heat rejection is done by keeping pressure constant.

• Carnot cycle is a theoretical cycle whereas the Rankine cycle is a practical one.

• Carnot cycle ensures the maximum efficiency under ideal conditions, but the Rankine cycle ensures the operation in real conditions.

• The efficiency obtained by the Rankine cycle is always lower than that of the Carnot cycle.

Carnot Cycle works with air whereas Rankine Cycle uses water/steam

Shortcomings of Carnot Cycle

1. the Carnot Vapor Cycle requires that the boiler and condensor operate isothermally, for this the heat transfer rates have to be infinitely large so as ensure that the heat transfer occurs at minimal time.

Shortcomings of Rankine cycle

1. the work done during the constant pressure process is less than that of the work done during the isothermal process. This is the reason for lower efficiency as compared to carnot cycle

B)

Increasing the boiler pressure increases the temperature of heat rejection therby inccreasing the thermal efficiency

C)

Increasing the mean temperature of heat addition improves the thermal efficiency

Increasing the mean temperature of reat rejection decreases the thermar efficiency

D)

Both the ideal Rankine and Brayton Cycles consist of two isentropic pressure change processes and two isobaric heat transfer processes . The major difference between the two is that the Rankine is a vapor cycle, where the working fluid is cycled between vapor and liquid states, while the Brayton is a gas cycle, where the working fluid always exists as a gas. The Rankine Cycle\'s T-s diagram includes the vapor dome while the Brayton Cycle\'s T-s diagram typically does not, as the Brayton Cycle occurs to the right of the vapor dome. Additionally, recall that isobaric phase-change processes are also isothermal, and thus the heat transfer process lines are horizontal inside the vapor dome for the Rankine Cycle.

F)

COP can never be less than one for a heat pump as it ceases to be a heat pump