A stationary gas-turbine power plant operates on an ideal regenerative Brayton cycle ($\epsilon$=100 percent) with air as the working fluid. Air enters the compressor at 95kPa and 290K and the turbine at 880kPa and 1100K. Heat is transferred to air from an external source at a rate of 30,000kJ/s. Determine the power delivered by this plant

(a) assuming constant specific heats for air at room temperature and

(b) accounting for the variation of specific heats with temperature.

A gas-turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers 32 MW of power. The minimum and maximum temperatures in the cycle are 310 and 900 K, and the pressure of air at the compressor exit is 8 times the value at the compressor inlet. Assuming an isentropic efficiency of 80 percent for the compressor and 86 percent for the turbine, determine the mass flow rate of air through the cycle. Account for the variation of specific heats with temperature.

A gas-turbine power plant operates on the regenerative Brayton cycle between the pressure limits of 100 and 700 kPa. Air enters the compressor at $30^{\circ} \mathrm{C}$ at a rate of 12.6 kg/s and leaves at $260^{\circ} \mathrm{C}.$ It is then heated in a regenerator to $400^{\circ} \mathrm{C}$ by the hot combustion gases leaving the turbine. A diesel fuel with a heating value of 42,000 kJ/kg is burned in the combustion chamber with a combustion efficiency of 97 percent. The combustion gases leave the combustion chamber at $871^{\circ} \mathrm{C}$ and enter the turbine, whose isentropic efficiency is 85 percent. Treating combustion gases as air and using constant specific heats at $500^{\circ} \mathrm{C},$ determine (a) the isentropic efficiency of the compressor. (b) the effectiveness of the regenerator, (c) the air-fuel ratio in the combustion chamber, (d) the net power output and the back work ratio, (e) the thermal efficiency, and (f) the second-law efficiency of the plant. Also determine (g) the second-law efficiencies of the compressor, the turbine, and the regenerator, and (h) the rate of the exergy flow with the combustion gases at the regenerator exit.

A gas-turbine power plant operates on a simple Brayton cycle with air as the working fluid. The air enters the turbine at 120 psia and 2000 R and leaves at 15 psia and 1200 R. Heat is rejected to the surroundings at a rate of 6400 Btu/s, and air flows through the cycle at a rate of 40 lbm/s. Assuming the turbine to be isentropic and the compressor to have an isentropic efficiency of 80 percent, determine the net power output of the plant. Account for the variation of specific heats with temperature.

A stationary gas-turbine power plant operates on an ideal regenerative Brayton cycle $(\varepsilon=100$ percent) with air as the working fluid. Air enters the compressor at 95 kPa and 290 K and the turbine at 880 kPa and 1100 K. Heat is transferred to air from an external source at a rate of 30,000 kJ/s. Determine the power delivered by this plant (a) assuming constant specific heats for air at room temperature and (b) accounting for the variation of specific heats with temperature.

A combined gas turbine-vapor power plant operates as shown in figure. Pressure and temperature data are given at principal states, and the net power developed by the gas turbine is $147\ \mathrm{MW}$. Using air-standard analysis for the gas turbine, determine (a) the net power, in MW, developed by the power plant. (b) the overall thermal efficiency of the plant. Develop a full accounting of the net rate of exergy increase of the air passing through the gas turbine combustor. Let $T_0=300 \mathrm{~K}, p_0=1\ \text{bar}$.

A stationary gas-turbine power plant operates on an ideal regenerative Brayton cycle $(\epsilon=100 \text { percent })$ with air as the working fluid. Air enters the compressor at 95 kPa and 290 K and the turbine at 880 kPa and 1100 K. Heat is transferred to air from an external source at a rate of 30,000 kJ/s. Determine the power delivered by this plant (a ) assuming constant specific heats for air at room temperature and (b ) accounting for the variation of specific heats with temperature.

A gas-turbine power plant operates on a simple Brayton cycle with air as the working fluid. The air enters the turbine at $800 \mathrm{~kPa}$ and $1100 \mathrm{~K}$ and leaves at $100 \mathrm{~kPa}$ and $670 \mathrm{~K}$. Heat is rejected to the surroundings at a rate of $6700 \mathrm{~kW}$, and air flows through the cycle at a rate of $18 \mathrm{~kg} / \mathrm{s}$. For what compressor efficiency will the gas-turbine power plant produce zero net work?

Consider a combination of a gas turbine power plant and a steam power plant, as shown in figure. The gas turbine operates at higher temperatures (thus called a topping cycle) than the steam power plant (then called a bottom cycle). Assume both cycles have a thermal efficiency of $32 \%$. What is the efficiency of the overall combination, assuming $Q_L$ in the gas turbine equals $Q_H$ to the steam power plant?

A Brayton cycle has air into the compressor at 95 kPa, 290 K, and has an efficiency of 50%. The exhaust temperature is 675 K. Find the pressure ratio and the specific heat addition by the combustion for this cycle.

An air-standard Diesel cycle has a compression ratio of 16 and a cutoff ratio of 2 . At the beginning of the compression process, air is at $95 kPa$ and $27^{\circ} C$. Accounting for the variation of specific heats with temperature, determine (a) the temperature after the heat-addition process, (b) the thermal efficiency, and (c) the mean effective pressure.

An inventor claims to have invented an adiabatic steady-flow device with a single inlet–outlet that produces 230 kW when expanding 1 kg/s of air from 1200 kPa and $300^\circ C$ to 100 kPa. Is this claim valid?

Consider a cold air-standard Diesel cycle. Operating data at principal states in the cycle are given in the table below. The states are numbered as in Fig. 9.5. For $k=1.4, c_v=$ $0.718 \mathrm{~kJ} /(\mathrm{kg} \cdot \mathrm{K})$, and $c_p=1.005 \mathrm{~kJ} /(\mathrm{kg} \cdot \mathrm{K})$, determine (a) the heat transfer per unit mass and work per unit mass for each process, in $\mathrm{kJ} / \mathrm{kg}$, and the cycle thermal efficiency. (b) the exergy transfers accompanying heat and work for each process, in $\mathrm{kJ} / \mathrm{kg}$. Devise and evaluate an exergetic efficiency for the cycle. Let $T_0=300 \mathrm{~K}$ and $p_0=100\ \mathrm{kPa}$.

$$\begin{array}{cccl} \text { State } & T(\mathrm{~K}) & p(\mathrm{kPa}) & v\left(\mathrm{~m}^3 / \mathrm{kg}\right) \\ \hline 1 & 340 & 100 & 0.9758 \\ 2 & 1030.7 & 4850.3 & 0.06098 \\ 3 & 2061.4 & 4850.3 & 0.1220 \\ 4 & 897.3 & 263.9 & 0.9758 \end{array}$$

A gas turbine for an automobile is designed with a regenerator. Air enters the compressor of this engine at 100 kPa and $30^{\circ} \mathrm{C}.$ The compressor pressure ratio is 10; the maximum cycle temperature is $800^{\circ} \mathrm{C};$ and the cold air stream leaves the regenerator $10^{\circ} \mathrm{C}$ cooler than the hot air stream at the inlet of the regenerator. Assuming both the compressor and the turbine to be isentropic, determine the rates of heat addition and rejection for this cycle when it produces 115 kW. Use constant specific heats at room temperature.