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# A system consists of 2 kg of carbon dioxide, (CO_2) gas initially at state 1, where P1=\ 100\ kPa,T_1=300\ k. The system undergoes a power cycle consi

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A system consists of 2 kg of carbon dioxide, $$\displaystyle{\left({C}{O}_{{2}}\right)}$$ gas initially at state 1, where $$\displaystyle{P}{1}=\ {100}\ {k}{P}{a},{T}_{{1}}={300}\ {k}$$. The system undergoes a power cycle consisting of the following processes:
Process 1-2: constant- volume to $$\displaystyle{P}_{{2}}={400}{k}{P}{a}$$
Process 2-3: expansion with $$\displaystyle{P}{V}^{{{1.28}}}$$ = constant
Process 3-1: constant-pressure compression
Assuming ideal gas model and neglecting kinetic and potentialenergy effects,
Sketch the cycle on a P-V diagram.
Calculate the work and the heat transfer for each process.

2021-02-22

STEP:1
$$\displaystyle{p}_{{1}}={100}{k}{p}{a}$$
$$\displaystyle{t}_{{1}}={300}{k}$$
1-2constant volume process
workdone=zero
STEP: 2
p2=400k
$$\displaystyle\text{Find }\ {t}_{{2}}$$
$$\displaystyle{\frac{{{p}_{{1}}{v}_{{1}}}}{{{t}_{{1}}}}}={\frac{{{p}_{{2}}{v}_{{2}}}}{{{t}_{{2}}}}}$$
Since $$\displaystyle{v}_{{1}}={v}_{{2}}$$
Find $$\displaystyle{t}_{{2}}$$
STEP: 3
2-3 is entropic process
work done=
$$\displaystyle{\frac{{{m}{R}{\left({T}_{{2}}-{T}_{{3}}\right)}}}{{{1}-{n}}}}$$
where $$n=1.28$$
STEP: 4
To find $$\displaystyle{t}_{{3}}$$ from the below equation.
$$\displaystyle{\left({\frac{{{T}_{{1}}}}{{{T}_{{3}}}}}\right)}={\left({\frac{{{p}_{{1}}}}{{{p}_{{2}}}}}\right)}^{{{\frac{{{n}}}{{{n}-{1}}}}}}$$
STEP: 5
3-1 constant pressure prosses
workdone=  $$\displaystyle{m}{R}{\left({t}_{{1}}-{t}_{{3}}\right)}$$