Water is the working fluid in an ideal Rankine cycle. Superheated vapor enters the turbine at 10 MPa, $480^\circ C,$ and the condenser pressure is 6 kPa. Isentropic efficiencies of the turbine and pump are 84% and 73%, respectively. Determine for the cycle a. the heat transfer to the working fluid passing through the steam generator, in kJ per kg of steam flowing. b. the thermal efficiency. c. the heat transfer from the working fluid passing through the condenser to the cooling water, in kJ per kg of steam flowing.

Water is the working fluid in an ideal Rankine cycle. Saturated vapor enters the turbine at 16 MPa, and the condenser pressure is 8 kPa. The mass flow rate of steam entering the turbine is 120 kg/s. Determine a. the net power developed, in kW. b. the rate of heat transfer to the steam passing through the boiler, in kW. c. the thermal efficiency. d. the mass flow rate of condenser cooling water, in kg/s, if the cooling water undergoes a temperature increase of $18^\circ C$ with negligible pressure change in passing through the condenser.

Water is the working fluid in an ideal Rankine cycle. The condenser pressure is. $6\ \mathrm{kPa}$, and saturated vapor enters the turbine at $10\ \mathrm{MPa}$. Delermine the heat transfer rates, in $\mathrm{kJ}$ per kg of steam flowing, for the working fluid passing through the boiler and condenser and calculate the thermal efficiency.

A power plant based on the Rankine cycle is under development to provide a net power output of $10\ \mathrm{MW}$. Solar collectors are to be used to generate Refrigerant 22 vapor at $1.6\ \mathrm{MPa}, 50^{\circ} \mathrm{C}$, for expansion through the turbine. Cooling water is available at $20^{\circ} \mathrm{C}$. Specify the preliminary design of the cycle and estimate the thermal efficiency and the refrigerant and cooling water flow rates, in $\mathrm{kgh}$.

Water is the working fluid in a Rankine cycle. Superheated vapor enters the turbine at $10 \mathrm{MPa}, 480^{\circ} \mathrm{C}$, and the condenser pressure is $6 \mathrm{kPa}$. The turbine and pump have isentropic efficiencies of 80 and $70 \%$, respectively. Determine for the cycle (a) the heat transfer to the working fluid passing through the steam generator, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam flowing. (b) the thermal efficiency. (c) the heat transfer from the working fluid passing through the condenser to the cooling water, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam flowing.

Water is the working fluid in an ideal regenerative Rankine cycle with one closed feedwater heater. Superheated vapor enters the turbine at $10 \mathrm{MPa}, 480^{\circ} \mathrm{C},$ and the condenser pressure is 6 kPa. Steam expands through the first-stage turbine where some is extracted and diverted to a closed feedwater heater at 0.7 MPa. Condensate drains from the feedwater heater as saturated liquid at 0.7 MPa and is trapped into the condenser. The feedwater leaves the heater at 10 MPa and a temperature equal to the saturation temperature at 0.7 MPa. Determine for the cycle a. the heat transfer to the working fluid passing through the steam generator, in kJ per kg of steam entering the first-stage turbine. b. the thermal efficiency. c. the heat transfer from the working fluid passing through the condenser to the cooling water, in kJ per kg of steam entering the first-stage turbine.

Water is the working fluid in an ideal Rankine cycle with reheat. Superheated vapor enters the turbine at $10\ \mathrm{MPa}$, $480^{\circ} \mathrm{C}$, and the condenser pressure is $6\ \mathrm{kPa}$. Steam expands through the first-stage turbine to $0.7\ \mathrm{MPa}$ and then is reheated to $480^{\circ} \mathrm{C}$. Determine for the cycle (a) the rate of heat addition, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam entering the first-stage turbine. (b) the thermal efficiency. (c) the rate of heat transfer from the working fluid passing through the condenser to the cooling water, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam entering the first-stage turbine.

Consider a solar-energy-powered ideal Rankine cycle that uses water as the working fluid. Saturated vapor leaves the solar collector at 150 psia, and the condenser pressure is 0.95 psia. Determine the thermal efficiency of this cycle.

Water is the working fluid in an ideal Rankine cycle. Superheated vapor enters the turbine at $10\ \mathrm{MPa}, 480^{\circ} \mathrm{C}$ and the condenser pressure is $6\ \mathrm{kPa}$. Determine for the cycle (a) the rate of heat transfer to the working fluid passing through the steam generator, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam flowing. (b) the thermal efficiency. (c) the rate of heat transfer from the working fluid passing through the condenser to the cooling water, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam flowing.

Water is the working fluid in an ideal Rankine cycle. The condenser pressure is 8 kPa, and saturated vapor enters the turbine at 11 MPa. Determine the heat transfer in kJ per kg of steam flowing, for the working fluid passing through the boiler and condenser and calculate the thermal efficiency.

An air-conditioning unit with a coefficient of performance of 2.93 provides $5000 \:Btu/h$ of cooling while operating during the cooling season 8 hours per day for 125 days. If you pay 10 cents per $kW \cdot h$ for electricity, determine the cost, in dollars, for the cooling season.

A window-mounted room air conditioner removes energy by heat transfer from a room and rejects energy by heat transfer to the outside air. For steady-state operation, the air conditioner cycle requires a power input of 0.434 kW and has a coefficient of performance of 6.22. Determine the rate that energy is removed from the room air, in kW. If electricity is valued at $\$0.1/kW \cdot h$, determine the cost of operation for 24 hours of operation.

For each function identify the domain and range, state the maximum and minimum values, identify the axis of symmetry, if it exists, and describe the end behavior. g(x) = x² + 2x + 1

Show that if a series is conditionally convergent, then the series obtained from its positive terms is divergent, and the series obtained from its negative terms is divergent.