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 is the specific temperature at which a real gas behaves most like an ideal gas over a range of pressures. At this temperature, the effects of attractive forces and repulsive forces approximately cancel each other out.

Step 2: Analyze the behavior of a real gas below Boyle's Temperature. Below \(T_B\), the attractive forces between gas molecules are dominant at moderate pressures. An increase in pressure makes it easier for molecules to come together, causing the volume to decrease more than it would for an ideal gas. This makes the product PV decrease initially. At very high pressures, repulsive forces become dominant, causing the volume to be larger than for an ideal gas, and the PV product increases. Thus, the PV vs P curve shows a dip (minimum).

Step 3: Analyze the behavior of a real gas above Boyle's Temperature. Above \(T_B\), the kinetic energy of the molecules is high, and the repulsive forces (due to molecular size) are dominant at all pressures. An increase in pressure results in a PV value that is always 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 accurately describes the behavior below Boyle's temperature, with an initial decrease followed by an increase. (D) Incorrect. PV is constant for an ideal gas, not a real gas above \(T_B\).