Lesson 7.4: Ideal & Real Gas Properties

Understanding gas properties is essential for thermodynamics and power engineering. GATE and PSU exams often test equations of state, compressibility, and deviations from ideal behavior.

🔹 1. Introduction

• Ideal Gas: Hypothetical gas following PV = nRT exactly

• Real Gas: Actual gases that deviate from ideal behavior at high pressure or low temperature

• Applications: Steam turbines, compressors, internal combustion engines, refrigeration

🔹 2. Ideal Gas Properties

• Equation of State:

$$PV=nRT\text{or}Pv=RT$$

Where P = pressure, V = volume, n = moles, R = universal gas constant, T = temperature

• Internal Energy (U) & Enthalpy (H): Functions of temperature only for ideal gases

dU=CvdT,dH=CpdTdU = C_v dT, \quad dH = C_p dTdU=Cv​dT,dH=Cp​dT

• Specific Heats Relation:

Cp−Cv=RC_p – C_v = RCp​−Cv​=R

• Compressibility Factor (Z): For ideal gas Z = 1

🔹 3. Real Gas Properties

• Deviations from Ideal Behavior: At high pressure and low temperature

• Compressibility Factor (Z):

Z=PvRTZ = \frac{P v}{R T}Z=RTPv​

• Equations of State for Real Gases:

  1. Van der Waals Equation:

(P+av2)(v−b)=RT\left(P + \frac{a}{v^2}\right)(v-b) = R T(P+v2a​)(v−b)=RT

Where a = intermolecular attraction, b = finite molecular volume

• Applications: High-pressure compressors, supercritical boilers, refrigeration cycles

🔹 4. Thermodynamic Properties & Relations

• Specific Heats (Cp, Cv) vary with temperature for real gases

• Internal Energy & Enthalpy corrections using compressibility factor or departure functions

• Isentropic Relations: For ideal gas:

PVγ=constant,TVγ−1=constantPV^\gamma = \text{constant}, \quad T V^{\gamma-1} = \text{constant}PVγ=constant,TVγ−1=constant

🔹 5. Solved Examples (PYQ Style)

1. Compute pressure of ideal gas at given T, V, n

2. Determine Z for real gas using Van der Waals equation

3. Calculate internal energy and enthalpy changes for ideal and real gases

4. Apply isentropic relations for turbines and compressors

🔹 6. Practice Exercises

1. Solve PV = nRT problems for ideal gases

2. Calculate compressibility factor Z for given P, V, T

3. Determine work done in isothermal expansion of ideal gas

4. Analyze deviation of real gas from ideal behavior

5. Solve thermodynamic cycles using ideal gas assumptions

🔹 7. Summary

• Ideal Gas: PV = nRT, U & H depend on temperature only

• Real Gas: Deviates from ideal behavior; Z ≠ 1, Van der Waals equation

• Applications: Engines, turbines, compressors, refrigeration

• Exam Tip: Questions often involve compressibility factor, real vs ideal gas, and property calculations