13468-10-59P AID: 1825 | 05/12/2014

Show the T-s diagram with steam as working fluid for the ideal Rankine cycle as in Figure (1).

Express the specific work input to the cycle.

(1)

Here, pressure at state 1 is , pressure at state 2 is , and specific volume of steam at state 1 is .

Refer to saturated water-pressure table, and interpret the values of , and for a pressure

Substitute for , for , and for in Equation (1).

Express the enthalpy of steam at state 2.

(2)

Here, specific enthalpy of steam at state 1 is , and specific enthalpy of steam at state 2 is .

Substitute for , and for in Equation (2).

Express the quality of steam at the end of heat rejection process.

(3)

Here, specific entropy of saturated liquid is, specific entropy of vaporization is , and specific entropy at state 4 is .

Refer to superheated water table, and interpret the values of and for a pressureand temperature .

Similarly, interpret the values of , and from saturated water-pressure table for a pressure .

Since , substitute for , for , and for in Equation (3).

Therefore, the quality of steam at the exit of turbine is .

Express the specific enthalpy of steam at state 4.

(4)

Refer to saturated steam tables, and interpret the value of for a pressure as .

Substitute for , for , and 0.7934 for in Equation (4).

Express the specific heat input to the Rankine cycle.

(5)

Here, specific heat input to the cycle is , specific enthalpy of steam at state 3 is .

Substitute for , and for in Equation (5).

Express the specific heat output of the Rankine cycle.

(6)

Here, specific heat output of the cycle is .

Substitute for , and for in Equation (6).

Express the exergy destruction for the process.

(7)

Here, entropy at state i is , entropy at state j is , heat transferred during the process is , and temperature of the heat source is , and ambient temperature is .

As processes , and are isentropic processes, the exergy destruction during the process remains constant. Therefore, the exergy destruction during processes , and are .

Process .

Substitute 290 K for , 1,500 K for , for , for , and for in Equation (7).

Therefore, the exergy destruction during process is .

Process .

Substitute 290 K for , 290 K for , for , for , and for in Equation (7).

Therefore, the exergy destruction during process is .