## Ideal Gas

What is the pressure inside a 200 m^3 tank if it is filled with 50 kg of nitrogen at 80°C? Note the universal gas constant is 8,314 J/(kmol∙K), and nitrogen has a molar mass of 28 kg/kmol.

##
__
__**Hint**

**Hint**

Ideal gas formula:

$$$PV=mRT$$$

where
$$P$$
is pressure,
$$V$$
is volume,
$$m$$
is the mass of gas,
$$R$$
is the gas constant, and
$$T$$
is the absolute temperature.

##
__
__**Hint 2**

**Hint 2**

To solve for the gas constant:

$$$R=\bar{R}/molecular \: weight$$$

where
$$\bar{R}$$
is the universal gas constant.

Ideal gas formula:

$$$PV=mRT$$$

where
$$P$$
is pressure,
$$V$$
is volume,
$$m$$
is the mass of gas,
$$R$$
is the gas constant, and
$$T$$
is the absolute temperature. Since
$$R=\bar{R}/molecular \: weight$$
, where
$$\bar{R}$$
is the universal gas constant:

$$$R=8,314\frac{J}{kmol\cdot K}\cdot \frac{kmol}{28kg}=297\:\frac{J}{kg\cdot K}$$$

Thus,

$$$P=\frac{mRT}{V}=\frac{(50kg)(297\frac{J}{kg\cdot K})(80+273K)}{200m^3}$$$

$$$=26,204\frac{J}{m^3}=26,204\frac{N\cdot m}{m^3}=26,204\frac{N}{m^2}=26\:kPa$$$

26 kPa