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First Law of Thermodynamics

5 moles of id...

Question

$5$ moles of ideal gas at temp. $T$ is compressed isothermally from $12$ atm to $24$ atm. Calculate the value of $10 r$ ,
where, $r = \frac{work done in reversible process}{work done in irreversible process}$
(Given : $ln 2 = 0.7$ )

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Solution

$r = \frac{W o r k d o n e a l o n g r e v e r s i b l e p r o c e s s}{W o r k d o n e a l o n g s i n g l e s t e p i r r e v e r s i b l e p r o c e s s}$

$= \frac{n R T \times l n (P_{f} / P_{i})}{24 \times (n R T / 12 - n R T / 24)} = l n 2 = 0.7;$

So, $10 r = 7$

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