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Thermodynamic Cycle: The Waitz Cycle, Exercises of Applied Thermodynamics

The waitz thermodynamic cycle, a closed-loop system used in refrigeration and cooling processes. The cycle consists of four legs: an adiabatic expansion (1-2), constant volume heat addition (2-3), constant pressure expansion (3-4), and isothermal compression (4-1). Information on the pressure, temperature, and specific volume changes for each leg, as well as the heat and work transfers. The net work for the cycle is negative, making it suitable for cooling applications.

Typology: Exercises

2011/2012

Uploaded on 07/22/2012

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T5 SOLUTIONS (Waitz)
a) Draw a thermodynamic cycle on p-v and T- v diagrams consisting of
Leg 1-2: adiabatic expansion
Leg 2-3: constant volume heat addition
Leg 3-4: constant pressure expansion
Leg 4-1: isothermal compression
Assume that all processes are quasi-static and involve an ideal gas.
Pressure (kPa)
l
ines of
c
onstant
t
emperature
1
3
4
2
For 1-2, pvγγ
γγ=constant
adiabat is steeper than
pv=constant (an
Temperature (Kelvin)
Specific Volume (m
3
/kg)
isotherm)
3
4
1
2
l
ines of
c
onstant
p
ressure
F
or 1-2, Tvγγ
γγ
11
11=constant
a
curved line much like the
a
diabat on a p-v diagram
b
ut it would be shallower
Specific Volume (m
3
/kg)
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T5 SOLUTIONS (Waitz)

a) Draw a thermodynamic cycle on p-v and T- v diagrams consisting of

Leg 1-2: adiabatic expansion Leg 2-3: constant volume heat addition Leg 3-4: constant pressure expansion Leg 4-1: isothermal compression

Assume that all processes are quasi-static and involve an ideal gas.

Pressure (kPa)

lines of constant temperature

For 1-2, pv γγγγ =constant

adiabat is steeper than pv=constant (an

Temperature (Kelvin)

Specific Volume (m^3 /kg)

isotherm)

lines of constant pressure

For 1-2, Tv γγγγ−−−−1^111 =constant

a curved line much like the adiabat on a p-v diagram but it would be shallower Specific Volume (m^3 /kg)

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b) For each leg determine if the heat and work transfers are (+), (-), or zero.

Q ( +, -, or zero) W ( + , -, or zero)

Leg 1 -2 0 +

Leg 2 -3 + 0

Leg 3 -4 + +

Leg 4 -1 -^ -

c) Is the net work for this cycle positive or negative?

The net work for this cycle is negative The area under the expansion process is less than the area under the compression processes.

d) What common purpose might you use a cycle like this for and why?

This cycle could serve as a cooler or refrigerator. Overall it takes in energy in the form of heat from cold temperatures and expels energy in the form of heat from high temperatures. The net work for the cycle as a whole is negative, meaning that energy is put into the system to enable these transfers of heat to take place.

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