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Two moles of ...

Question

Two moles of an ideal monoatomic gas at $27^{o}$ C occupies a volume of $V$ . If the gas is expanded adiabatically to the volume $2 V$ , then the work?

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Solution

$w = - P (V_{2} - V_{1})$
$P V = n R T$
$P = \frac{n R T}{V}$
$W = - (\frac{n R T}{V}) (2 V - V)$
$W = - n R T$
$n = 2$
$T = 273 + 27 = 300$

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