Question

Evaluate the volume occupied by 7.000 kg of air at a gage ressure of 623 kPa and a temperature of 686 C. Calculate air density undet the same conditions.

Answer 1

Question #78265, Engineering / Chemical Engineering

Evaluate the volume occupied by 7.000 kg of air at a gage ressure of 623 kPa and a temperature of 686 C. Calculate air density under the same conditions.

Solution

Considering air ideal gas.

$$pV = nRT \Leftrightarrow V = \frac{nRT}{p},$$

where $p$ is pressure, in Pa;

$R$ is gas constant; $R = 8.31 \, \text{J/MK}$;

$T$ is the absolute temperature, in K;

$n$ is the number of moles; $n = \frac{m}{M}$ ($m$ is mass, $M$ is molar mass; $M = 28.9647 \, \text{g/mol}$)

$$V = \frac{mRT}{Mp} = \frac{7.000 \times 8.31 \times (686 + 273)}{28.9647 \times 10^{-3} \times 623 \times 10^{3}} = 3.09 \, \text{m}^3$$

Answer: $3.09 \, \text{m}^3$.

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