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Compressibility Factor

One mole of a...

Question

One mole of an ideal gas undergoes a process $P = P_{0} {(1 + {(\frac{2 V_{0}}{V})}^{2}]}^{- 1},$ where $P_{0}, V_{0}$ are constants. Change in temperature of the gas when volume is changed from $V = V_{0}$ to $V = 2 V_{0}$ is $\frac{n P_{o} V_{0}}{R}$ . Then $n$ is

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Solution

$P = P_{0} {(1 + {(\frac{2 V_{0}}{V})}^{2}]}^{- 1} A t V = V_{0}, P = \frac{P_{0}}{5} T_{i} = \frac{P V}{n R} = \frac{(\frac{P_{0}}{5}) V_{0}}{n R} = \frac{P_{0} V_{0}}{5 n R} A t V = 2 V_{0}, P = \frac{P_{0}}{2} T_{f} = \frac{P V}{n R} = \frac{(\frac{P_{0}}{2}) 2 V_{0}}{n R} = \frac{P_{0} V_{0}}{n R} Δ T = T_{f} - T_{i} = \frac{4 P_{0} V_{0}}{5 n R}$

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