Which of the following is not true about density of the gases?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 25-01-2018 (Morning Shift)
Detailed Explanation
Gases are highly compressible fluids whose thermodynamic state is described by an equation of state. Their mass density fluctuates considerably with thermal and barometric changes.
From the ideal gas equation of state:
\[ P V = m R T \;\implies\; \rho = \frac{m}{V} = \frac{P}{R T} \]
Therefore, mass density \(\rho\) is directly proportional to absolute pressure \(P\), inversely proportional to absolute temperature \(T\), and inversely proportional to volume \(V\).
Why “Do not depend on temperature and pressure” Is Correct
Statement (d) asserts that gas density does not depend on temperature and pressure, which is completely false according to the ideal gas law \(\rho = P / (RT)\).
Why the Other Options Are Wrong
- A. Proportional to pressure: Density is directly proportional to pressure (at constant T), which is true.
- B. Inversely proportional to temperature: Density is inversely proportional to absolute temperature (at constant P), which is true.
- C. Inversely proportional to volume: For a fixed mass of gas, density is inversely proportional to volume (ρ = m/V), which is true.
Key Point
Gas density depends strongly on state: ρ = P / (RT); proportional to pressure and inversely to temperature.
Key Concepts for Students
- Standard air density at sea level (15°C, 101.3 kPa) is ≈ 1.225 kg/m³.
- Universal gas constant R_u = 8314 J/(kmol·K); specific gas constant for air R = 287 J/(kg·K).
- Liquids are nearly incompressible, whereas gas density varies dramatically with pressure and temperature.
Practice more: this is question 41 in Properties of Fluid MCQs – Part 3. Try the whole set and check every answer instantly.