A power cycle operating at steady state receives energy by heat transf

Joanna Benson 2021-12-15 Answered
A power cycle operating at steady state receives energy by heat transfer at a rate Q˙H at TH=18000K and regects
energy by heat transfer to a cold reservoir at a rate Q˙C at Tc=600K. For each of the following cases, determine
whether the cycle operates reversibly, operates irreversibly, or is impossible.
a. Q˙H=500kW,Q˙C=100kW
b. Q˙H=500kW,W˙ cyc≤=250kW,Q˙C=200kW
c. W˙=350kW,Q˙C=150kW
d. Q˙H=500kW,Q˙C=200kW
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Expert Answer

Thomas Nickerson
Answered 2021-12-16 Author has 32 answers
The maximum efficiency in the cycle is defined as;
ηmax=1TCTH
In our case TC=600K and TH=1800K, which is maximum efficiency of:
ηmax=2366.7%
The actual efficiency cant

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Elaine Verrett
Answered 2021-12-17 Author has 41 answers
Hot reservoir temperature TH=1800K
Cold reservoir temperature Te=600K
a)
Heat transfer at hot reservoir QH=500KW
Heat transfer at cold reservoir QC=100KW
b
Heat transfer at hot reservoir QH=500KW
Heat transfer at cold reservoir QC=200KW
Cycle work W˙cyc=250KW
c)
Cycle work Wcyc=350KW˙
Heat transfer at cold reservoir QC=150KW
d)
Heat transfer at hot reservoir QH=500KW
Heat transfer at cold reservoir QC=200KW
Required
Determine whether the cycle operates reversibly, operates irreversibly, or is impossible
Assumption
Constant average values is used
a)
Maximum net work could be defined by
Wcyc=QHQC
⇒=500100=400KW
Maximum efficiency check
{Wmax}=1TeTH
16001800=0.6667=66.67%
{Wavtual}=WcycQH
400500=0.8=80%
At actual efficiency is higher than maximum efficiency then the cycle is not possibe.
b)
Maximum work check.
Wcyc=QHQC
⇒=500200=300KW
As actual work is higher than the maximum work the cycle is not possible.
Maximum efficiency check
{Wmax}=1TeTH
16001800=0.6667=66.67%
{Wavtual}=WcycQH
250500=0.5=50%
As actual efficiency is lower than maximum efficiency then the cycle operates irreversibly.
Then the cycle is not possible.
c)
Heat added from hot reservoir could be calculated as following.
QH=Wcyc+Qe
⇒=350+150=500KW
Maximum efficiency check.
{Wmax}=1TeTH
16001800=0.6667=66.67%

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