Internal energy of the van der Waals gas

Oxygen with density p = 120 kg/m under a pressure of 10 MPa is in a pressure vessel. Considering oxygen under such pressure to be a van der Waals gas, find its temperature T and compare it with analogous calculations in the framework of an ideal gas. The van der Waals constants are (a) = 0.136 N m /mole (f) = 3.17.10 m /mole. 

Solution Write the van der Waals equation for any amount of the substance v 

Considering the oxygen in the pressure vessel as an ideal gas, we can obtain from the ideal gas equation 

Although the difference in temperatures is not so high (16 K), it can, nevertheless, be significant at precise experiments. 

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