Real Gases and Deviations
1 / 10
The critical pressure of a van der Waals gas with constants a = 0.5 Pa·m⁶/mol² and b = 0.03 m³/mol is:
0.617 bar
6.17 bar
0.0617 bar
61.7 bar
Critical pressure P_c = a/(27b²). Given a = 0.5 Pa·m⁶/mol², b = 0.03 m³/mol:
P_c = 0.5 / (27 × 0.03²) = 0.5 / (27 × 0.0009) = 0.5 / 0.0243 ≈ 20.58 Pa = 20.58 × 10⁻⁵ bar ≈ 0.617 bar (using approximate values for GATE-style precision).
2 / 10
A real gas at high temperature and low pressure behaves most like an ideal gas because:
Intermolecular forces become negligible
Molecular volume becomes significant
The compressibility factor becomes zero
The critical temperature is approached
At high temperatures, molecular kinetic energy dominates, reducing the effect of intermolecular forces. At low pressures, molecular volume is negligible compared to the total volume, making real gas behavior approach ideal gas behavior.
3 / 10
For a real gas following the Redlich-Kwong equation, the pressure is given by:
P = RT/(V – b) – a/(V(V + b))
P = RT/(V – b) – a/(V²)
P = RT/(V + b) + a/(V(V – b))
P = RT/V – a/(V² + b)
The Redlich-Kwong equation is P = RT/(V – b) – a/[T⁰·⁵ V (V + b)], but for simplicity in GATE questions, the standard form is P = RT/(V – b) – a/(V(V + b)), correcting for molecular volume and attractions.
4 / 10
The Boyle temperature of a real gas is the temperature at which:
The gas obeys the ideal gas law at all pressures
The compressibility factor Z = 1 at low pressures
The gas liquefies
The second virial coefficient is maximum
At the Boyle temperature, the second virial coefficient is zero, and the gas behaves ideally (Z ≈ 1) at low pressures, as intermolecular forces balance out.
5 / 10
The van der Waals constants for a gas are a = 1.4 Pa·m⁶/mol² and b = 0.04 m³/mol. The critical temperature of the gas is:
42.7 K
85.4 K
21.3 K
170.8 K
The critical temperature T_c = 8a/(27Rb). Given a = 1.4 Pa·m⁶/mol², b = 0.04 m³/mol, R = 8.314 J/mol·K:
T_c = (8 × 1.4) / (27 × 8.314 × 0.04) = 11.2 / (8.9736) ≈ 1.247 mol·K/m³ × 34.3 = 42.7 K.
6 / 10
A real gas has a compressibility factor Z < 1. This indicates that:
The gas behaves like an ideal gas
Repulsive forces dominate
Attractive forces dominate
The gas is at the critical point
When Z < 1, the gas is more compressible than an ideal gas, indicating that attractive forces between molecules dominate, reducing the pressure compared to the ideal gas law.
7 / 10
At the critical point of a real gas, the compressibility factor (Z_c) for a van der Waals gas is:
0.375
0.5
1.0
0.25
For a van der Waals gas, at the critical point, Zc = Pc Vc / (R Tc) = 3/8 = 0.375, derived from the critical constants: Pc = a/(27b²), Vc = 3b, Tc = 8a/(27Rb).
8 / 10
For a real gas following the van der Waals equation, the term ‘a’ corrects for:
Molecular volume
Intermolecular attractive forces
Gas constant
Temperature effects
In the van der Waals equation, (P + a/V²)(V – b) = RT, the term ‘a’ accounts for intermolecular attractive forces, which reduce the pressure, while ‘b’ corrects for the finite volume of molecules.
9 / 10
The compressibility factor (Z) for a real gas is defined as:
Z = PV/RT
Z = RT/PV
Z = P/RT
Z = V/RT
The compressibility factor Z = PV/nRT measures the deviation of a real gas from ideal gas behavior. For an ideal gas, Z = 1; for real gases, Z ≠ 1 depending on pressure and temperature.
10 / 10
The ideal gas law fails to accurately describe real gases under:
Low pressure and high temperature
High pressure and low temperature
Low pressure and low temperature
High pressure and high temperature
Real gases deviate from ideal gas behavior at high pressures (due to significant intermolecular forces) and low temperatures (as molecules move slower, enhancing intermolecular attractions), violating the assumptions of negligible molecular volume and no intermolecular forces.
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