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Class 11 Physics Chapter 11: Thermodynamics case study question with answers

One case-based question of the kind CBSE-pattern school exams ask: a passage, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.

Case study · 4 marks
Arjun inflates his cycle tyre with a hand pump. He notices that after a few quick strokes the lower end of the pump barrel feels warm. In one quick stroke, 0.020 mol of air at 300 K in the barrel is pushed into two-thirds of its volume before the valve opens. The stroke is so fast that almost no heat leaves the air, and air may be treated as an ideal gas with γ = 1.4. His sister points out that if he pumps very slowly, the barrel stays near room temperature. (R = 8.3 J mol⁻¹ K⁻¹, (1.5)0.4 = 1.176)
Part 1 · 1 mark
The barrel grows warm in quick strokes mainly because
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Answer: (c) the work done on the air raises its internal energy, and in a quick stroke it has no time to lose heat

A quick stroke is nearly adiabatic: ΔQ ≈ 0, so the work done on the air (W < 0) increases U and the temperature rises (T₂ > T₁).

Part 2 · 1 mark
The temperature of the air at the end of the stroke is about
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Answer: (c) 353 K

TV^(γ−1) is constant: T₂ = 300 × (1.5)0.4 = 300 × 1.176 ≈ 353 K. 450 K takes T ∝ 1/V; 200 K takes T ∝ V; 300 K assumes no change.

Part 3 · 2 marks
Find the work done on the air in this stroke.
Answer and marking scheme

Work done by the gas in an adiabatic change is W = μR(T₁ − T₂)/(γ − 1) = 0.020 × 8.3 × (300 − 352.8)/0.4 ≈ −21.9 J. So about 21.9 J of work is done on the air, all of which raises its internal energy.

  • W = μR(T₁ − T₂)/(γ − 1) used (1)
  • about 21.9 J done on the air (1)
Or
Name the process that very slow pumping approximates, and say whether it needs more or less work than a quick stroke for the same compression, giving a reason.
Answer and marking scheme

Slow pumping lets heat flow out to the barrel and the room, so the air stays near room temperature: the compression is nearly isothermal. For the same reduction in volume the adiabatic is steeper (slope −γP/V against −P/V), so its pressure rises faster and more work is needed in a quick stroke; the slow, isothermal compression needs less work.

  • nearly isothermal (1)
  • less work, as the adiabatic is steeper and its pressure rises faster (1)
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