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Standard XII

Chemistry

Percentage Composition

Two litres of...

Question

Two litres of $N_{2}$ at $0^{0}$ C and $5$ atm are expanded exothermally against a constant external pressure of $1$ atm until the pressure of gas reaches $1$ atm. Assuring gas to be ideal. Calculate work of expansion?

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Solution

By Boyle's law,

$P_{1} V_{1} = P_{2} V_{2}$

$P_{1} = 5 a t m, P_{2} = 1 a t m, V_{1} = 2 L$

$V_{2} = \frac{5 a t m \times 2 L}{1 a t m}$

$V_{2} = 10 L$

Now, Work -
$w = P_{e x t .} Δ V$

$w = - 1 a t m (10 - 2) L$ (Ext. pressure $= 1 a t m$ )

$w = - 8 a t m . L$

Therefore,
$- 8 a t m . L = (\frac{101.325}{1 a t m L}) \times 8 = - 810.6 J$ ( $1 a t m L = 101.325$ )

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