## 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
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 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