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 simple Brayton cycle between the pressure limits of 100 and 800 kPa. Air enters the compressor at $30^{\circ} \mathrm{C}$ and leaves at $330^{\circ} \mathrm{C}$ at a mass flow rate of 200 kg/s. The maximum cycle temperature is 1400 K. During operation of the cycle, the net power output is measured experimentally to be 60 MW. Assume constant properties for air at 300 K with $c_{v}=0.718 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}, c_{p}=$ $1.005 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}, R=0.287 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}, k=1.4$. (a) Sketch the T-s diagram for the cycle. (b) Determine the isentropic efficiency of the turbine for these operating conditions. (c) Determine the cycle thermal efficiency.

A gas-turbine power plant operating on the simple Brayton cycle has a pressure ratio of 7. Air enters the compressor at $0^{\circ} \mathrm{C}$ and 100 kPa. The maximum cycle temperature is 1500 K. The compressor has an isentropic efficiency of 80 percent, and the turbine has an isentropic efficiency of 90 percent. Assume constant properties for air at 300 K with $c_{v}=0.718 \mathrm{kJ} / \mathrm{kg} \cdot K,\ c_{p}=1.005 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K},\ R=0.287 \mathrm{kJ} / \mathrm{kg} \cdot \mathrm{K}$ k=1.4. (a) Sketch the T-s diagram for the cycle. (b) If the net power output is 150 MW, determine the volume flow rate of the air into the compressor in $\mathrm{m}^{3} / \mathrm{s}.$ (c) For a fixed compressor inlet velocity and flow area, explain the effect of increasing compressor inlet temperature (i.e., summertime operation versus wintertime operation) on the inlet mass flow rate and the net power output with all other parameters of the problem being 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 95 kPa and 290 K and the turbine at 760 kPa and 1100 K. Heat is transferred to air at a rate of 35,000 kJ/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.

Consider a simple ideal Brayton cycle with air as the working fluid. The pressure ratio of the cycle is $6$ , and the minimum and maximum temperatures are $300$ and $1300 \mathrm{~K}$, respectively. Now the pressure ratio is doubled without changing the minimum and maximum temperatures in the cycle. Calculate the change in $(a)$ the net work output per unit mass and $(b)$ the thermal efficiency of the cycle as a result of this modification. Assume variable specific heats for air.

A turbojet is flying with a velocity of 900 ft/s at an altitude of 20,000 ft, where the ambient conditions are 7 psia and $10^{\circ} \mathrm{F}$. The pressure ratio across the compressor is 13, and the temperature at the turbine inlet is 2400 R. Assuming ideal operation for all components and constant specific heats for air at room temperature, determine (a) the pressure at the turbine exit, (b) the velocity of the exhaust gases, and (c) the propulsive efficiency.

Consider an ideal Ericsson cycle with air as the working fluid executed in a steady-flow system. Air is at $27^{\circ} \mathrm{C}$ and 120 kPa at the beginning of the isothermal compression process, during which 150 kJ/kg of heat is rejected. Heat transfer to air occurs at 1200 K. Determine (a) the maximum pressure in the cycle, (b) the net work output per unit mass of air, and (c) the thermal efficiency of the cycle.

An ideal Brayton cycle with regeneration has a pressure ratio of 10. Air enters the compressor at 300 K and the turbine at 1200 K. If the effectiveness of the regenerator is 100 percent, determine the net work output and the thermal efficiency of the cycle. Account for the variation of specific heats with temperature.

A $4-\mathrm{m}$ $\times 5-\mathrm{m} \times 6-\mathrm{m}$ room is to be heated by a baseboard resistance heater. It is desired that the resistance heater be able to raise the air temperature in the room from $7$ to $23^{\circ} \mathrm{C}$ within $15 \mathrm{~min}$. Assuming no heat losses from the room and an atmospheric pressure of $100 \mathrm{~kPa}$, determine the required power of the resistance heater. Assume constant specific heats at room temperature.

A container filled with 45 kg of liquid water at 95$^\circ{}$C is placed in a 90-m^3 room that is initially at 12$^\circ{}$C. Thermal equilibrium is established after a while as a result of heat transfer between the water and the air in the room. Using constant specific heats, determine (a) the final equilibrium temperature, (b) the amount of heat transfer between the water and the air in the room, and (c) the entropy generation. Assume the room is well sealed and heavily insulated.

An ideal vapor-compression refrigeration cycle operates at steady state with Refrigerant 134a as the working fluid. Saturated vapor enters the compressor at 2 bar, and saturated liquid exits the condenser at 8 bar. The mass flow rate of refrigerant is 7 kg/min. Determine a. the compressor power, in kW. b. the refrigerating capacity, in tons. c. the coefficient of performance.

simple ideal Rankine cycle with water as the working fluid operates between the pressure limits of 3 MPa in the boiler and 30 kPa in the condenser. If the quality at the exit of the turbine cannot be less than 85 percent, what is the maximum thermal efficiency this cycle can have?

Air enters the compressor of a gas-turbine engine at $300 \mathrm{~K}$ and $100\ \mathrm{kPa}$, where it is compressed to $700\ \mathrm{kPa}$ and $580 \mathrm{~K}$. Heat is transferred to the air in the amount of $950 \mathrm{~kJ} / \mathrm{kg}$ before it enters the turbine. For a turbine efficiency of $86$ percent, find $(a)$ the fraction of the turbine work output used to drive the compressor and $(b)$ the thermal efficiency. Use constant specific heat at room temperature.

An $825\text{~g}$ iron block is heated to $352{ }^{\circ} \mathrm{C}$ and placed in an insulated container (of negligible heat capacity) containing $40.0 \mathrm{~g}$ of water at $20.0^{\circ} \mathrm{C}$. What is the equilibrium temperature of this system? If your answer is $100^{\circ} \mathrm{C}$, find the amount of water that has vaporized. The average specific heat of iron over this temperature range is $560 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K})$.