The GATE Grind

GATE 2023 ME – Question 41

Thermodynamics · Ideal and real gases · 2 marks · Multiple choice

Which one of the following statements is FALSE?

  1. For an ideal gas, the enthalpy is independent of pressure.
  2. For a real gas going through an adiabatic reversible process, the process equation is given by $PV^\gamma$ = constant, where P is the pressure, V is the volume and $\gamma$ is the ratio of the specific heats of the gas at constant pressure and constant volume.
  3. For an ideal gas undergoing a reversible polytropic process $PV^{1.5}$ = constant, the equation connecting the pressure, volume and temperature of the gas at any point along the process is $\frac{P}{R} = \frac{mT}{V}$, where $R$ is the gas constant and $m$ is the mass of the gas.
  4. Any real gas behaves as an ideal gas at sufficiently low pressure or sufficiently high temperature.

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Show answer and explanation

Correct answer: (B) For a real gas going through an adiabatic reversible process, the process equation is given by $PV^\gamma$ = constant, where P is the pressure, V is the volume and $\gamma$ is the ratio of the specific heats of the gas at constant pressure and constant volume.

Explanation

The relation $PV^\gamma = $ constant for an adiabatic reversible process holds for an ideal gas with constant specific heats. For a real gas it does not hold in general, so statement B is false. Statement A is true because the enthalpy of an ideal gas depends only on temperature. Statement C is just the ideal gas law $PV = mRT$ written in another form, valid at every point of any process of an ideal gas. Statement D is true because real gases approach ideal behaviour at low pressure and high temperature.