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Q.

The final volume (lit) of one mole of an ideal gas initially at $27 ° C$ and $8.21$ atm pressure, if it absorbs 420 cal of heat during a reversible isothermal expansion____ $(\log 2 = 0.3)$

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answer is 6.

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Detailed Solution

As $q = - W$
$W = - n R T \ln \frac{P_{2}}{P_{1}}$
$- 420 = - n R T \ln (\frac{8.21}{P})$
$420 = 1 \times 2 \times 300 \ln (\frac{8.21}{P}) \Rightarrow P = \frac{8.21}{2}$
But $P V = n R T \Rightarrow \frac{8.21}{2} \times V = 1 \times 0.0821 \times 300$
$\Rightarrow V = 6 l t$

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The final volume (lit) of one mole of an ideal gas initially at 27°C and 8.21 atm pressure, if it absorbs 420 cal of heat during a reversible isothermal expansion____(log2=0.3)