A gas refrigeration system using air as the working fluid has a pressure ratio of 5. Air enters the compressor at 0°C. The high-pressure air is cooled to 35°C by rejecting heat to the surroundings. The refrigerant leaves the turbine at -80°C and then it absorbs heat from the refrigerated space before entering the regenerator. The mass flow rate of air is 0.4 kg/s. Assuming isentropic efficiencies of 80 percent for the compressor and 85 percent for the turbine and using constant specific heats at room temperature, determine...

a.) The effectiveness of the regenerator

b.) The refrigeration load

c.) The COP of the cycle

d.) The refrigeration load and the COP if this system operated on the simple gas refrigeration cycle. Use the same compressor inlet temperature as given, the same turbine inlet temperature as calculated, and the same compressor and turbine efficiencies.

## Wednesday, May 10, 2006

### HW #9, P#8 - Performance of a Two-Stage Cascade Refrigeration System - 8 pts

Consider a two-stage cascade refrigeration system operating between the pressure limits of 1.2 MPa and 200 kPa with refrigerant-134a as the working fluid. Heat rejection from the lower cycle to the upper cycle takes place in an adiabatic counterflow heat exchanger where the pressure in the upper and lower cycles are 0.4 and 0.5 MPa, respectively. In both cycles, the refrigerant is a saturated liquid at the condenser exit and a saturated vapor at the compressor inlet, and the isentropic efficiency of the compressor is 80 percent. If the mass flow rate of the refrigerant through the lower cycle is 0.15 kg/s, determine...

a.) The mass flow rate of the refrigerant through the upper cycle

b.) The rate of heat removal from the refrigerated space

c.) The COP of this refrigerator

a.) The mass flow rate of the refrigerant through the upper cycle

b.) The rate of heat removal from the refrigerated space

c.) The COP of this refrigerator

### HW #9, P#7 - Performance of a Geothermal Heat Pump - 6 pts

A heat pump with refrigerant-134a as the working fluid is used to keep a space at 25°C by absorbing heat from geothermal water that enters the evaporator at 50°C at a rate of 0.065 kg/s and leaves at 40°C. The refrigerant enters the evaporator at 20°C with a quality of 23 percent and leaves at the inlet pressure as saturated vapor. The refrigerant loses 300 W of heat to the surroundings as it flows through the compressor and the refrigerant leaves the compressor at 1.4 MPa at the same entropy as the inlet. Determine...

a.) The degrees of subcooling of the refrigerant in the condenser

b.) The mass flow rate of the refrigerant

c.) The heating load and the COP of the heat pump

d.) The theoretical minimum power input to the compressor for the same heating load

a.) The degrees of subcooling of the refrigerant in the condenser

b.) The mass flow rate of the refrigerant

c.) The heating load and the COP of the heat pump

d.) The theoretical minimum power input to the compressor for the same heating load

### HW #9, P#6 - Ideal Brayton Cycle with Reheating and Multistage Compression - 8 pts

Consider an ideal Brayton cycle with two stages of compression and two stages of expansion. The pressure ratio across each stage of the compressor and turbine is 3. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. Determine the back work ratio and the thermal efficiency of the cycle. Use variable specific heats. Solve this problem assuming...

a.) no regenerator is used

b.) a regenerator with 75% effectiveness is used

a.) no regenerator is used

b.) a regenerator with 75% effectiveness is used

### HW #9, P#5 - Effects of Reheating and Multistage Compression on the Efficiency of a Brayton Cycle - 2 pts

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.) 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?

### HW #9, P#4 - Thermal Efficiency of an Air-Standard Cycle - 6 pts

An air-standard cycle is executed in a closed system and is composed of the following four processes:

1-2 Isentropic compression from 100 kPa and 27°C to 1 MPa

2-3 P constant heat addition in amount of 2800 kJ/kg

3-4 Heat rejection at constant specific volume 100 kPa

4-1 Heat rejection at constant pressure back to the initial state

Assuming constant specific heats at room temperature...

a.) Show the cycle on PV and TS diagrams

b.) Calculate the maximum temperature in the cycle

c.) Determine the thermal efficiency.

1-2 Isentropic compression from 100 kPa and 27°C to 1 MPa

2-3 P constant heat addition in amount of 2800 kJ/kg

3-4 Heat rejection at constant specific volume 100 kPa

4-1 Heat rejection at constant pressure back to the initial state

Assuming constant specific heats at room temperature...

a.) Show the cycle on PV and TS diagrams

b.) Calculate the maximum temperature in the cycle

c.) Determine the thermal efficiency.

### HW #9, P#3 - NEW NEW NEW - Non-Ideal Binary Ammonia-Steam Rankine Power Cycle - 10 pts

A binary vapor power cycle consists of two Rankine Cyles with steam and ammonia as the working fluids. In the steam cycle, superheated vapor enters the turbine at 900 lbf/in2 and 1100°F. Saturated liquid leaves the condenser at 140°F. The heat rejected from the steam cycle is provided to the ammonia cycle. Saturated ammonia vapor enters the ammonia turbine at 120°F. Saturated liquid leaves the ammonia condenser at 75°F. Each turbine has an sentropic efficiency of 90% and the pumps operate isentropically. The net power output of the binary cycly is 7 x 107 Btu/h.

a.) Determine the quality of each turbine effluent.

b.) Determine the mass flow rate of each working fluid in lbm/h.

c.) Determine the thermal efficiency of the binary power cycle.

a.) Determine the quality of each turbine effluent.

b.) Determine the mass flow rate of each working fluid in lbm/h.

c.) Determine the thermal efficiency of the binary power cycle.

### HW #9, P#2 - Ideal Reheat rankine Cycle - 10 pts

Steam enters the high-pressure turbine of a steam power plant that operates on the ideal reheat Rankine cycle at 800 psia and 900°F and leaves as saturated vapor. Steam is then reheated to 800°F before it expands to a pressure of 1psia. Heat is transferred to the steam in the boiler at a rate of 6 104 Btu/s. Steam is cooled in the condenser by the cooling water from a nearby river, which enters the condenser at 45°F. Show the cycle on a TS diagram with respect to saturation lines, and determine...

a.) The pressure at which reheating takes place

b.) The net power output and thermal efficiency

c.) The minimum mass flow rate of the cooling water required

a.) The pressure at which reheating takes place

b.) The net power output and thermal efficiency

c.) The minimum mass flow rate of the cooling water required

### HW #9, P#1 - Effect of Boiler Pressure on Rankine Cycle Performance - 3 pts

Consider a simple ideal Rankine Cycle with fixed condenser pressure. Assume that the boiler always produces saturated steam and the condenser always produces saturated liquid water. What is the effect of increasing the boiler pressure on...

a.) Pump work input

b.) Turbine work output

c.) Heat supplied

d.) Heat rejected

e.) Cycle efficiency

f.) Moisture content at turbine exit

Multiple choice: Increases, Decreases or Remains the Same

a.) Pump work input

b.) Turbine work output

c.) Heat supplied

d.) Heat rejected

e.) Cycle efficiency

f.) Moisture content at turbine exit

Multiple choice: Increases, Decreases or Remains the Same

### HW #8, P#8 - Entropy Generation and Lost Work in an Evaporator - 10 pts

Air enters the evaporator section of a window air conditioner at 100 kPa and 37°C with a volumetric flow rate of 10 m3/min. The refrigerant, R134a at 150 kPa with a quality of 0.3 enters the evaporator at a rate of 0.8 kg/min and leaves as saturated vapor at the same pressure. Determine the exit temperature of the air and the rate of entropy generation for this process ...

a.) Assuming the outer surfaces of the air conditioner are perfectly insulated

b.) Assuming heat is transferred to the evaporator of the air conditioner from the surrounding medium at 37 °C at a rate of 30 kJ/min.

c.) The lost work in kW, for both parts (a) and (b).

a.) Assuming the outer surfaces of the air conditioner are perfectly insulated

b.) Assuming heat is transferred to the evaporator of the air conditioner from the surrounding medium at 37 °C at a rate of 30 kJ/min.

c.) The lost work in kW, for both parts (a) and (b).

### HW #8, P#7 - Shaft Work Requirment for Single-Stage and Two-Stage Compressors - 6 pts

Air enters a two-stage compressor at 100 kPa and 27°C and is compressed to 900 kPa. The pressure ratio across each stage is the same, and the air is cooled to the initial temperature between the two stages. Assuming the compression process to be isentropic, determine the power input to the compressor for a mass flow rate of 0.02 kg/s. What would your answer be if only one stage of compression were used?

### HW #8, P#6 - Entropy Generation and Lost Work in a Mixing Chamber - 6 pts

Liquid water at 200 kPa and 20°C is heated in a chamber by mixing it with superheated steam at 200 kPa and 150°C. Liquid water enters the mixing chamber at a rate of 2.5 kg/s, and the chamber is estimated to lose heat to the surrounding air at 25°C at a rate of 1200 kJ/min. If the mixture leaves the mixing chamber at 200 kPa and 60°C, determine... (a) and (b) .

a.) The mass flow rate of the superheated steam

b.) The rate of entropy generation during this mixing process

c.) The lost work in kW

a.) The mass flow rate of the superheated steam

b.) The rate of entropy generation during this mixing process

c.) The lost work in kW

### HW #8, P#5 - Entropy Generation and Lost Work Due to Heat Loss From an Iron - 2 pts

A 1000 W iron is left on the ironing board with its base exposed to the air which is at 20oC. If the surface of the iron is at 400oC, determine:

a.) The total rate of entropy generation during this process in steady operation

b.) How much of this entropy generation occurs within the iron ? (Sgen,int)

c.) The lost work in kW, assuming the temperature of the surroundings is 20oC

a.) The total rate of entropy generation during this process in steady operation

b.) How much of this entropy generation occurs within the iron ? (Sgen,int)

c.) The lost work in kW, assuming the temperature of the surroundings is 20oC

### HW #8, P#4 - Entropy Generation and Lost Work in a Double-Pipe HEX - 6 pts

Cold water (cp = 4.18 kJ/kg · °C) leading to a shower enters a well-insulated, thin-walled, double-pipe, counter-flow heat exchanger at 15°C at a rate of 0.25 kg/s and is heated to 45°C by hot water (cp = 4.19 kJ/kg · °C) that enters at 100°C at a rate of 3 kg/s. Determine ...

a.) the rate of heat transfer

b.) the rate of entropy generation in the heat exchanger

c.) The lost work in kW, assuming the temperature of the surroundings is 20oC

a.) the rate of heat transfer

b.) the rate of entropy generation in the heat exchanger

c.) The lost work in kW, assuming the temperature of the surroundings is 20oC

### HW #8, P#3 - Use of Isentropic Efficiency in the Analysis of a Real Turbine - 6 pts

Steam enters an adiabatic turbine at 7 MPa, 600°C, and 80 m/s and leaves at 50 kPa, 150°C, and 140 m/s. If the power output of the turbine is 6 MW, determine...

a.) the mass flow rate of the steam flowing through the turbine

b.)the isentropic efficiency of the turbine

a.) the mass flow rate of the steam flowing through the turbine

b.)the isentropic efficiency of the turbine

### HW #8, P#2 - Performance of a Reversible Compressor Along Different Process Paths - 8 pts

Nitrogen gas is compressed from 80 kPa and 27°C to 480 kPa by a 10-kW compressor. Determine the mass flow rate of nitrogen through the compressor, assuming the compression process to be ...

a.) isentropic

b.) polytropic with n = 1.3

c.) isothermal

d.) ideal two-stage polytropic with n = 1.3

a.) isentropic

b.) polytropic with n = 1.3

c.) isothermal

d.) ideal two-stage polytropic with n = 1.3

### HW #8, P#1 - Shaft Work for a Compressor vs. a Pump - 6 pts

Saturated refrigerant-134a vapor at 15 psia is compressed reversibly in an adiabatic compressor to 80 psia. Determine the work input to the compressor. What would your answer be if the refrigerant were first condensed at constant pressure before it was compressed?

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