Calculate the efficiency of a Rankine cycle that is modified from the parameters used in the text in each of the following three ways (one at a time), and comment briefly on the results: (a) reduce the maximum temperature to $500°\text{C}$; (b)reduce the maximum pressure to 100 bars; (c)reduce the minimum temperature to $10°\text{C}$.

A Rankine cycle operates between temperatures $20°\text{C}$and $500°\text{C}$at maximum pressure 300 bars.

The efficiency of Rankine cycle is given by

$\text{e}=1-\frac{{\text{H}}_4{\text{-H}}_1}{{\text{H}}_3{\text{-H}}_1}$

Here, ${\text{H}}_1$is enthalpy at point 1, ${\text{H}}_3$is enthalpy at point 3, and ${\text{H}}_4$is enthalpy at point 4 in the below Rankine cycle.

The entropy of the superheated steam is expressed as follows:

${\text{S}}_4\text{=x}\left({\text{S}}_{water}\right)\text{+}\left(1-\text{x}\right){\text{S}}_{steam}$

where,

$$\begin{gathered} {\text{S}}_{water}\text{=Entropyofsaturatedwater} \\ {\text{S}}_{steam}\text{=Entropyofsaturatedsteam} \\ \text{x=fractionofwater} \end{gathered}$$

So, $\text{x=}\frac{{\text{S}}_4{\text{-S}}_{\text{steam}}}{{\text{S}}_{water}{\text{-S}}_{\text{steam}}}$

Similarly enthalpy at point 4: $H_4\text{=x}\left({\text{H}}_{water}\right)\text{+}\left(1-\text{x}\right){\text{H}}_{steam}$.

where

$$\begin{gathered} {\text{H}}_{water}\text{=Enthalpyofsaturatedwater} \\ {\text{H}}_{steam}\text{=Enthlapyofsaturatedsteam} \\ \text{x=fractionofwater} \end{gathered}$$

Here,

$$\begin{gathered} {\text{S}}_4{\text{=5.971KJ·K}}^{-1}{\text{·kg}}^{-1} \\ {\text{S}}_{water}{\text{=0.297KJ·K}}^{-1}{\text{·kg}}^{-1} \\ {\text{S}}_{steam}{\text{=8.667KJ·K}}^{-1}{\text{·kg}}^{-1} \end{gathered}$$

So,

$$\begin{gathered} \text{x=}\frac{5.971-8.667}{0.297-8.667} \\ \text{=0.344} \end{gathered}$$

Now,

$$\begin{gathered} \text{x=0.344} \\ {\text{H}}_{\text{water}}\text{=84KJ/kg} \\ {\text{H}}_{steam}\text{=2538KJ/kg} \end{gathered}$$

So,

Hence,

$$\begin{gathered} \text{e=1-}\frac{1693.8-84}{3081-84} \\ =0.463 \end{gathered}$$

The efficiency of Rankine cycle is 0.463 when the maximum temperature is reduced to$500°\text{C}$.

A Rankine cycle operates between temperatures and at maximum pressure 300 bars.

The efficiency of Rankine cycle is given by

Here, is enthalpy at point 1, is enthalpy at point 3, and is enthalpy at point 4 in the below Rankine cycle.

The entropy of the superheated steam is expressed as follows:

where,

So,

Similarly enthalpy at point 4: .

where