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# Calculate the temperature of 4.0 mol of a gas occupying 5 dm^3 at 3.32 bar.

5.12     Calculate the temperature of $4.0 \: mol$ of a gas occupying $5\: \: dm^{3}$ at 3.32 bar.
$(R = 0.083 \: bar\: dm^{3} K^{-1} mol^{-1}).$

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We have the ideal gas equation,

$PV=nRT$

Pressure, p=3.32bar

Volume, V=5 $\dpi{100} dm^3$

Number of moles, n=4 mol

Gas constant R= 0.083

Temperature,  T=?

$T = \frac{PV}{nR} = \frac{3.32bar\times 5\ dm^3}{4\ mol\times 0.083 bar\ dm^3\ K^{-1}mol^{-1}} = 50K$

so, temperature, T=50K

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