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Exam level2 past questions

Ideal Gas Law and Equation

Learn the ideal gas equation, its relation to physical quantities like pressure, volume, temperature, and density, and its use in describing the behavior of ideal gases.

Why this shows up in the exam

NEET often asks you to use the ideal gas law in calculations and to relate it to other thermodynamic concepts.

How NEET tests this

Numerical · 2 QsApplicationDirect recall

Learn the idea

When an ideal gas follows a special relation like PV² = constant, combining it with the ideal gas equation shows that the product V·T stays constant, so V and T vary inversely.

🧠 Memory hook: Think of VT as a seesaw: when the volume goes up, the temperature must come down to keep the balance steady.

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • For a fixed amount of gas, pressure × volume = number of moles × R × temperature (ideal gas law)
  • Density ρ = mass/volume = (n M₀)/V, so P = ρ R_specific T where R_specific = R/M₀
  • Given PV² = C, dividing by V gives P V = C/V → using ideal gas law leads to V T = constant
  • In any closed‑system process, the amount of gas n does not change
  • R is a universal constant (8.314 J mol⁻¹ K⁻¹)

How to approach it

  1. 1Write the ideal gas law for the gas
  2. 2Replace P from the given relation (PV² = C) into the ideal gas law
  3. 3Simplify to obtain a relation that involves only V and T
  4. 4Identify the constant product and infer how V and T change relative to each other

Worked example — watch it click

An ideal gas follows a process described by the equation PV² = C from the initial (P₁, V₁, T₁) to the final (P₂, V₂, T₂) thermodynamic states, where C is a constant. Then:

  • A)If P₁ > P₂, then T₁ < T₂.
  • B)If V₂ > V₁, then T₂ > T₁.
  • ✅If V₂ > V₁, then T₂ < T₁.
  • D)If P₁ > P₂, then V₁ > V₂.

The concept behind this problem

The question asks you to link the process equation PV² = C with the ideal‑gas description, revealing that VT does not change, so a larger volume forces a lower temperature.

Step by step

  1. 1Given PV²=C and ideal gas PV=nRT, we get V²(nRT/V)=C, so VT=C/nR=constant.
  2. 2Therefore VT=constant, meaning if V increases, T must decrease.
  3. 3If V₂>V₁, then T₂<T₁.

Watch out

Many students forget the VT = constant result and wrongly claim that a larger volume always means a higher temperature.

Common slip-ups that cost marks

  • •Treating n as variable in a closed‑system question – it stays fixed
  • •Cancelling V incorrectly and losing the V² term
  • •Assuming temperature follows pressure directly without using the derived VT = constant

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 2NEET 2022

An ideal gas follows a process described by the equation PV² = C from the initial (P₁, V₁, T₁) to the final (P₂, V₂, T₂) thermodynamic states, where C is a constant. Then:

Push further

More challenging

2 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 2

A sealed container with a fixed volume of 5 litres holds an ideal gas at 27°C and 3 atm pressure. If the temperature is increased to 127°C, what is the final pressure inside the container? (Assume R = 8.31 J mol⁻¹ K⁻¹).

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