For perfect gas, the equation of state is              

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JKSSB JE Civil Jal Shakti 5 Dec 2022 Official Paper (Shift 2)
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  1. p/\(\rho\) = (RT)2
  2. p/P = (RT)2
  3. P*\(\rho\) = RT
  4. P/\(\rho\) = RT

Answer (Detailed Solution Below)

Option 4 : P/\(\rho\) = RT
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Concept:

A hypothetical gas that obeys the law PV = nR̅T at all pressures and temperatures is called Ideal gas. There are two equations for Ideal Gas.

  • PV = nR̅T
  • PV = mRT,
  • P/ρ = RT

where,

P = Absolute pressure (Pa), V = Volume (m3), n = Number of moles of the gas \( = \frac{{\bf{m}}}{{\bf{M}}}\)

\({\bar{R}} = \;\)Universal gas constant (8314 J/kg-mol.K), T = Absolute Temperature (K)

\(R = characteristic\;gas\;constant = \frac{{\bar R}}{M}\;\left( {\frac{J}{{kg.K}}} \right)\), M = Molecular weight of the gas

m = Mass of gas (kg) & ρ = Density of gas (kg/m3).

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