A steam turbine operates adiabatically at steady state. The operating conditions are given in the figure below. Determine the change in the specific entropy in kJ/K per kg of steam 1 2 T State 1: $P_1 = 15 bar$ Sat. Vap. State 2: $x = 85 \%$ $T_2 = 65 °C$
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Steam at $6000 \mathrm{kPa}$ and $500^{\circ} \mathrm{C}$ enters a steady-flow turbine. The steam expands in the turbine while doing work until the pressure is $1000 \mathrm{kPa}$. When the pressure is $1000 \mathrm{kPa}$ 10 percent of the steam is removed from the turbine for other uses. The remaining 90 percent of the steam continues to expand through the turbine while doing work and leaves the turbine at $10 \mathrm{kPa}$. The entire expansion process by the steam through the turbine is reversible and adiabatic. (a) Sketch the process on a $T-s$ diagram with respect to the saturation lines. Be sure to label the data states and the lines of constant pressure. (b) If the turbine has an isentropic efficiency of 85 percent, what is the work done by the steam as it flows through the turbine per unit mass of steam flowing into the turbine, in $\mathrm{kJ} / \mathrm{kg}$ ?
Steam enters a turbine operating at steady state at a pressure of $3 \mathrm{MPa}$, a temperature of $400^{\circ} \mathrm{C}$, and a velocity of $160 \mathrm{~m} / \mathrm{s}$. Saturated vapor exits at $100^{\circ} \mathrm{C}$, with a velocity of $100 \mathrm{~m} / \mathrm{s}$. Heat transfer from the turbine to its surroundings takes place at the rate of $30 \mathrm{~kJ}$ per kg of steam at a location where the average surface temperature is $350 \mathrm{~K}$. (a) For a control volume including only the turbine and its contents, determine the work developed, in $\mathrm{kJ}$, and the rate at which entropy is produced, in $\mathrm{kJ} / \mathrm{K}$, each per $\mathrm{kg}$ of steam flowing. (b) The steam turbine of part (a) is located in a factory where the ambient temperature is $27^{\circ} \mathrm{C}$. Determine the rate of entropy production, in $\mathrm{kJ} / \mathrm{K}$ per $\mathrm{kg}$ of steam flowing, for an enlarged control volume that includes the turbine and enough of its immediate surroundings so that heat transfer takes place from the control volume at the ambient temperature. Explain why the entropy production value of part (b) differs from that calculated in part (a).
Using Entropy
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Steam enters a steady-flow turbine with a mass flow rate of $13 \mathrm{kg} / \mathrm{s}$ at $600^{\circ} \mathrm{C}, 8 \mathrm{MPa}$, and a negligible velocity. The steam expands in the turbine to a saturated vapor at $300 \mathrm{kPa}$ where 10 percent of the steam is removed for some other use. The remainder of the steam continues to expand to the turbine exit where the pressure is $10 \mathrm{kPa}$ and quality is 85 percent. If the turbine is adiabatic, determine the rate of work done by the steam during this process.
Penny R.
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