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.

Air enters the compressor of a regenerative gasturbine engine at 310 K and 100 kPa, where it is compressed to 900 kPa and 650 K. The regenerator has an effectiveness of 80 percent, and the air enters the turbine at 1400 K. For a turbine efficiency of 90 percent, determine (a) the amount of heat transfer in the regenerator and (b ) the thermal efficiency. Assume variable specific heats for air.

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.

Develop an expression for the thermal efficiency of an ideal Brayton cycle with an ideal regenerator of effectiveness 100 percent. Use constant specific heats at room temperature.

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 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?

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 compresssor 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 simple ideal Brayton cycle without regeneration is modified to incorporate multistage compression with intercooling and multistage expansion with reheating, without changing the pressure or temperature limits of the cycle. As a result of these two modifications. (a) Does the net work output increase, decrease, or remain the same? (b) Does the back work ratio increase, decrease, or remain the same? (c) Does the thermal efficiency increase, decrease, or remain the same? (d) Does the heat rejected increase, decrease, or remain the same?

A stationary gas-turbine power plant operates on a simple ideal Brayton cycle with air as the working fluid. The air enters the compressor at 95kPa and 290K and the turbine at 760kP and 1100K. Heat is transferred to air at a rate of 35,000kJ/s.

Determine the power delivered by this plant

(a) assuming constant specific heats 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 $T_0=300 \mathrm{~K}, p_0=1\ \text{bar}$.

An air-standard Diesel cycle has a compression ratio of 18.2. Air is at $120^{\circ} \mathrm{F}$ and 14.7 psia at the beginning of the compression process and at 3200 R at the end of the heat- addition process. Accounting for the variation of specific heats with temperature, determine (a) the cutoff ratio, (b) the heat rejection per unit mass, and (c) the thermal efficiency.

The compression ratio of an ideal dual cycle is 14. Air is at 100 kPa and 300 K at the beginning of the compression process and at 2200 K at the end of the heal-addition process. Heat transfer to air takes place partly at constant volume and partly at constant pressure, and it amounts to 1520.4 kJ/kg. Assuming variable specific heats for air, determine (a) the fraction of heat transferred at constant volume and (b) the thermal efficiency of the cycle.

Use the General Power Rule to find the derivative of the function. $f(x)=\left(4 x-x^{2}\right)^{3}$

Write the equation of each sphere. The center is at (2,1,-2) and the sphere is tangent to the xy -plane.