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
• B. Low pressure and low temperature
• C. Low pressure and high temperature
• D. Double the temperature, double the pressure

Answer 1

The correct option is C Low pressure and high temperature

Van der Waals' equation of state is given as:
$(P+\frac{n^{2}a}{V^2})(V-nb)=nRT.....\left(1\right)$
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 $\left(1\right)$,
$V-nb\to V$
When the molecules are far apart, number density tends to zero. As a result, the inter-molecular attractive forces are negligible.
Thus in $\left(1\right)$,
$\frac{n^{2}a}{V^2}\to 0$
$\therefore \left(1\right)$ will be reduced to the ideal gas equation $PV=nRT$.
Hence, option (c) is the correct answer.