Superheated steam at 8 MPa and 480^∘ C leaves the steam generator of a vapor power plant. Heat t

step 1 Catosol is an excretion we have that the H2S is equals to HF2 plus X2S HFG 2. We got it as 173 b

Superheated steam at 8 MPa and 480^∘ C leaves the steam...

Superheated steam at $8 \mathrm{MPa}$ and $480^{\circ} \mathrm{C}$ leaves the steam generator of a vapor power plant. Heat transfer and frictional effects in the line connecting the steam generator and the turbine reduce the pressure and temperature at the turbine inlet to $7.6 \mathrm{MPa}$ and $440^{\circ} \mathrm{C}$, respectively. The pressure at the exit of the turbine is $10 \mathrm{kPa}$, and the turbine operates adiabatically. Liquid leaves the condenser at $8 \mathrm{kPa}, 36^{\circ} \mathrm{C}$. The pressure is increased to $8.6 \mathrm{MPa}$ across the pump. The turbine and pump isentropic efficiencies are $88 \%$. The mass flow rate of steam is $79.53 \mathrm{~kg} / \mathrm{s}$. Determine (a) the net power output, in $\mathrm{kW}$. (b) the thermal efficiency. (c) the rate of heat transfer from the line connecting the steam generator and the turbine, in $\mathrm{kW}$. (d) the mass flow rate of condenser cooling water, in $\mathrm{kg} / \mathrm{s}$, if the cooling water enters at $15^{\circ} \mathrm{C}$ and exits at $35^{\circ} \mathrm{C}$ with negligible pressure change.

Superheated steam at $8 \mathrm{MPa}$ and $480^{\circ} \mathrm{C}$ leaves the steam generator of a vapor power plant. Heat transfer and frictional effects in the line connecting the steam generator and the turbine reduce the pressure and temperature at the turbine inlet to $7.6 \mathrm{MPa}$ and $440^{\circ} \mathrm{C}$, respectively. The pressure at the exit of the turbine is $10 \mathrm{kPa}$, and the turbine operates adiabatically. Liquid leaves the condenser at $8 \mathrm{kPa}, 36^{\circ} \mathrm{C}$. The pressure is increased to $8.6 \mathrm{MPa}$ across the pump. The turbine and pump isentropic efficiencies are $88 \%$. The mass flow rate of steam is $79.53 \mathrm{~kg} / \mathrm{s}$. Determine
(a) the net power output, in $\mathrm{kW}$.
(b) the thermal efficiency.
(c) the rate of heat transfer from the line connecting the steam generator and the turbine, in $\mathrm{kW}$.
(d) the mass flow rate of condenser cooling water, in $\mathrm{kg} / \mathrm{s}$, if the cooling water enters at $15^{\circ} \mathrm{C}$ and exits at $35^{\circ} \mathrm{C}$ with negligible pressure change.

Key Concepts

Cooling Water Flow Calculation

Determining the mass flow rate of cooling water requires an energy balance that accounts for the specific heat capacity of water and its temperature change as it absorbs heat. This calculation ensures that the cooling system is properly sized to remove the necessary amount of heat from the condenser, maintaining efficient operation of the cycle.

Heat Transfer Rate Calculation

The calculation of heat transfer rates involves applying energy balance principles, where the rate of heat lost or gained is determined by the mass flow rate and the specific enthalpy change of the working fluid. This concept is essential for quantifying losses in pipelines and other components and for designing effective heat exchangers.

Adiabatic Process

An adiabatic process is one in which no heat is exchanged with the surroundings, meaning that all energy changes within the system are due to work interactions. This assumption simplifies the analysis of processes like turbine expansion, where it is often used to approximate the behavior of the system despite the presence of practical irreversibilities.

Thermal Efficiency

Thermal efficiency in power cycles represents the ratio of net work output to the heat input. It is a key performance metric that indicates how effectively the system converts supplied heat into useful work, thereby providing insight into the overall energy conversion performance of the power plant.

Superheated Steam

Superheated steam is produced when water is heated beyond its boiling point at a given pressure, resulting in a vapor that is no longer in equilibrium with liquid water. This state improves turbine efficiency by avoiding condensation during expansion, which can damage turbine blades and lower the overall work output.

Rankine Cycle

The Rankine cycle is the idealized cycle for steam power plants, consisting of four main processes: pressurization of the working fluid in a pump, heating (and often superheating) in a boiler, expansion through a turbine to produce work, and condensation in a condenser before the cycle repeats. It serves as a fundamental model for energy conversion in thermal power systems.

Isentropic Efficiency

Isentropic efficiency quantifies the performance of turbomachinery and pumps by comparing the actual work output (or input) to the ideal work output (or input) obtained under isentropic (constant entropy) conditions. This concept helps in assessing the real-world performance losses due to irreversibilities such as friction and non-ideal fluid behavior.

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