Blow up a balloon and it expands. Heat a sealed gas cylinder and its pressure climbs fast. Both follow one rule linking a gas’s pressure, volume, and temperature. That rule is the ideal gas law, and it drives almost every question about heat engines, compressors, and sound in air.
MCQ Questions🏛️ Must Know
The Ideal Gas Law and Kinetic Theory
- Ideal Gas Law An ideal gas obeys PV = nRT at every stage of any process. P is pressure, V is volume, n is the number of moles, and T is absolute temperature.
- Gas Constant R is the universal gas constant. Its value is 8.314 J/(mol·K), the same for every ideal gas.
- Three Older Laws The ideal gas law combines three simpler laws. Boyle's law says P is inversely proportional to V at constant T.
- Charles and Avogadro Charles's law says V is directly proportional to T at constant P. Avogadro's law says V is directly proportional to n, the mole count, at fixed P and T.
- Kinetic Theory Kinetic theory explains gas pressure using molecular motion. Molecules move randomly in straight lines and collide elastically with the walls and each other.
- Core Assumptions Molecule volume is treated as negligible next to the container's volume. Molecules exert no force on each other except during a collision.
📘 Good to Know
Specific Heats, Degrees of Freedom, and Gamma
- Cv Cv is the molar specific heat of a gas at constant volume. It is the heat needed to raise one mole by 1 K, with volume held fixed.
- Cp Cp is the molar specific heat at constant pressure. Cp is always larger than Cv, because some heat also does work expanding the gas.
- Mayer's Relation For an ideal gas, Cp minus Cv equals R. This is called Mayer's relation.
- Degrees of Freedom Each degree of freedom adds (1/2)R to a gas's molar specific heat. This comes from the law of equipartition of energy.
- Monatomic Gas A monatomic gas, like helium or argon, has 3 degrees of freedom (translation only). Its Cv is (3/2)R and its Cp is (5/2)R.
- Diatomic Gas A diatomic gas, like oxygen or nitrogen, adds 2 rotational degrees of freedom near room temperature. Its Cv is (5/2)R and its Cp is (7/2)R.
- Gamma Gamma (γ) is the ratio Cp/Cv, called the adiabatic index. It is 5/3 for a monatomic gas and 7/5 for a diatomic gas.
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🌟 Great to Know
Polytropic Processes and the Speed of Sound
- Polytropic Process A polytropic process follows PVⁿ = constant, for some fixed exponent n. Different values of n describe different named processes.
- Isothermal An isothermal process has n = 1, and temperature stays constant throughout. It reduces to Boyle's law, PV = constant.
- Isobaric An isobaric process has n = 0, and pressure stays constant. Volume and temperature then change together, following Charles's law.
- Isochoric An isochoric process has n approaching infinity, and volume stays fixed. All the heat added goes into raising temperature and pressure, none into expansion work.
- Adiabatic An adiabatic process has n = γ, and no heat enters or leaves the gas. It follows PVγ = constant, sometimes called Poisson's law.
- Speed of Sound Sound in a gas travels at c = √(γRT/M), where M is the gas's molar mass. Speed depends on temperature, not on pressure alone.
- Laplace's Correction Newton first assumed sound travels isothermally, which gave a speed too low to match experiments. Laplace corrected this, showing sound compression is adiabatic, adding the γ term.
📝 Exam Point of View
NDA & NA (I) 2026 GAT — Three Ideal-Gas-Process Questions
- Question NDA & NA (I) 2026, General Ability Test, Q54 gave an ideal gas following PV² = constant, with temperatures T1, T2 and volumes V1, V2. It asked which ratio T1/T2 is correct. The correct answer is T1/T2 = V2/V1.
Why Combining PV = nRT with the process rule PV² = constant gives TV = constant at every stage. So T1V1 = T2V2, which rearranges straight to T1/T2 = V2/V1 — a direct application of the polytropic-process idea above.
Link See the full question, NDA & NA (I) 2026 GAT, Q54. - Question NDA & NA (I) 2026 GAT Q55 described a process P = kT, for a constant k, and asked what the gas's molar heat capacity C equals in this process. The correct answer is C = Cv.
Why P = kT means P/T stays fixed, so V = nRT/P = nR/k also stays fixed. A process at constant volume is isochoric, and Cv is defined as the heat capacity of an isochoric process.
Link See the full question, NDA & NA (I) 2026 GAT, Q55. - Question NDA & NA (I) 2026 GAT Q62 asked for the ratio of the speed of sound in a gas before and after its pressure is doubled, with temperature held constant. The correct answer is a ratio of 1, meaning the speed does not change.
Why The speed-of-sound formula c = √(γRT/M) contains only temperature, not pressure. Pressure and density rise together at constant T, and their effects on speed cancel exactly.
Link See the full question, NDA & NA (I) 2026 GAT, Q62.
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