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Question

Under which of the following conditions is the law PV=RT obeyed most closely by a real gas?

A
High pressure and high temperature
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B
Low pressure and low temperature
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C
Low pressure and high temperature
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D
Double the temperature, double the pressure
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Solution

The correct option is C Low pressure and high temperature
Van der Waals' equation of state is given as:
(P+n2aV2)(Vnb)=nRT .....(1)
At low pressure and high temperature, the molecules are farther apart so that the volume of the molecules is negligible as compared to the size of the vessel.
Thus in (1),
VnbV
When the molecules are far apart, number density tends to zero. As a result, the inter-molecular attractive forces are negligible.
Thus in (1),
n2aV20
(1) will be reduced to the ideal gas equation PV=nRT.
Hence, option (c) is the correct answer.

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