Question

Saturated steam is generated in a boiler by converting a saturated liquid to a saturated vapor at 200 psia. This is done by transferring heat from the combustion gases, which are at \(500^{\circ} \mathrm{F}\), to the water in the boiler tubes. Calculate the wasted work potential associated with this heat transfer process. How does increasing the temperature of the combustion gases affect the work potential of steam stream? Take \(T_{0}=\) \(80^{\circ} \mathrm{F}\) and \(P_{0}=14.7\) psia.

Short answer

The effect of increasing the temperature of combustion gases on the work potential of the steam stream is that it increases the amount of heat transferred to the water, leading to a higher entropy generation and higher wasted work potential, which means lower efficiency of the process. However, it also results in a higher quality steam, which can enhance the performance of steam turbines in practical applications.

Step-by-step solution

Find the heat transferred to the water.

Using the given pressure and temperature of the combustion gases, we can look up the enthalpy of the superheated steam (\(h_g\)) at 200 psia and \(500^{\circ}\mathrm{F}\) from the steam tables. Similarly, we can find the enthalpy of saturated liquid (\(h_f\)) at 200 psia from the steam tables. \(h_g = 1204.4 \,\mathrm{Btu/lbm}\) (from steam tables for 200 psia and \(500^{\circ}\mathrm{F}\))\newline \(h_f = 393.32 \,\mathrm{Btu/lbm}\) (from steam tables for 200 psia and saturated liquid)\newline The amount of heat transferred from the combustion gases to the water during the process can be calculated using the equation: \(Q_{1-2} = m (h_g - h_f)\) (where m is the mass of water)

Find the entropy generation during the process.

Entropy generation can be determined from the equation: \(\Delta S_{1-2} = m \left( s_g - s_f \right) + \frac{Q_{1-2}}{T_0}\) (where \(s_g\) and \(s_f\) are the specific entropy of the saturated vapor and saturated liquid, respectively, at 200 psia) We can find the values of \(s_g\) and \(s_f\) from the steam tables for 200 psia: \(s_g = 1.7006 \,\mathrm{Btu/(lbm \cdot R)}\)\newline \(s_f = 0.6935 \,\mathrm{Btu/(lbm \cdot R)}\) Now, we can calculate the entropy generation \(\Delta S_{1-2}\).

Calculate the wasted work potential associated with the heat transfer process.

The wasted work potential can be calculated using the equation: \(W_\mathrm{lost} = T_0 \Delta S_{1-2}\) Substitute the values of \(T_0\) and \(\Delta S_{1-2}\) into the equation to find the wasted work potential.

Discuss the effect of increasing the temperature of combustion gases on the work potential of the steam stream.

Increasing the temperature of the combustion gases will increase the amount of heat transferred to the water. As a result, the entropy generation will also increase, leading to a higher wasted work potential. This means that the efficiency of the process will decrease, as a significant portion of work potential will be lost due to the higher temperature of combustion gases. On the other hand, increasing the temperature of the combustion gases will result in a higher quality steam, which can enhance the performance of the steam turbines in practical applications.