Argon is compressed in a polytropic process with nn = 1.2 from 120 kPa and 30∘ C to 1200 kPa in a piston-cylinder device. Determine the final temperature of the argon.

The polytropic relation is used to obtain the solution:PV−n=C&nbsp;P1V1−n=P2V2−n&nbsp;P11−nT1−n=P21−nT2−n&nbsp;T2=T1(P2P1)n−1n&nbsp;=303⋅(1200120)1.2−11.2K&nbsp;=445K=172∘C&nbsp;Result:&nbsp;T2=445K=172∘C

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puntgewelb5

Answered question

2021-11-11

Argon is compressed in a polytropic process with nn = 1.2 from 120 kPa and

30^{\circ}

C to 1200 kPa in a piston-cylinder device. Determine the final temperature of the argon.

Answer & Explanation

Florence Pittman

Beginner2021-11-12Added 15 answers

The polytropic relation is used to obtain the solution:
$\frac{P}{V^{- n}} = C$
$\frac{P_{1}}{V_{1}^{- n}} = \frac{P_{2}}{V_{2}^{- n}}$
$\frac{P_{1}^{1 - n}}{T_{1}^{- n}} = \frac{P_{2}^{1 - n}}{T_{2}^{- n}}$
$T_{2} = T_{1} {(\frac{P_{2}}{P_{1}})}^{n - \frac{1}{n}}$
$= 303 \cdot {(\frac{1200}{120})}^{1.2 - \frac{1}{1.2}} K$
$= 445 K = 172^{\circ} C$
Result:
$T_{2} = 445 K = 172^{\circ} C$

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