Question

Choose the CORRECT statement about the behavior of product PV against pressure for real gas. [where P is pressure and V is volume]

• A. Below Boyle's temperature, the value of PV first increases with increase in pressure, reaches a maximum value at a particular temperature and then begins to decrease
• B. Above Boyle's temperature, the value of PV continuously decreases with increase in pressure.
• C. Below Boyle's temperature, the value of PV first decreases with increase in pressure, reaches a minimum value at a particular temperature and then begins to increase.
• D. Above Boyle's temperature, the value of PV is almost constant with increase in pressure.

Hint:

Remember the PV vs. P isotherm graphs: - Above \(T_B\): PV steadily increases with P. - At \(T_B\): PV is nearly constant for a range of low pressures, then increases. - Below \(T_B\): PV first decreases, reaches a minimum, and then increases.

Answer 1

The Correct Option is C

Step 1: Define Boyle's Temperature (\(T_B\)). Boyle's temperature, \(T_B\), is the temperature where a real gas most closely resembles an ideal gas across a range of pressures. At \(T_B\), attractive and repulsive forces within the gas nearly balance.

Step 2: Analyze real gas behavior below Boyle's Temperature. Below \(T_B\), attractive forces dominate at moderate pressures. Increasing pressure causes a greater volume decrease than in an ideal gas, leading to an initial decrease in the PV product. At very high pressures, repulsive forces become dominant, and the PV product increases. Consequently, the PV vs P curve exhibits a dip (minimum).

Step 3: Analyze real gas behavior above Boyle's Temperature. Above \(T_B\), high molecular kinetic energy makes repulsive forces dominant at all pressures. Increasing pressure always results in a PV value greater than that of an ideal gas, and PV continuously increases with P.

Step 4: Evaluate the options. (A) Incorrect. PV first decreases, then increases below \(T_B\). (B) Incorrect. PV continuously increases above \(T_B\). (C) Correct. This correctly describes the behavior below Boyle's temperature, featuring an initial decrease followed by an increase. (D) Incorrect. PV is constant for an ideal gas, not a real gas above \(T_B\).