Paper I — Q5
(a) Assume that the Earth's atmosphere is pure nitrogen in thermodynamic equilibrium at a temperature of 300 K. Calculate the…
Assume that the Earth's atmosphere is pure nitrogen in thermodynamic equilibrium at a temperature of 300 K. Calculate the height above sea level at which the density of the atmosphere is one-half its sea level value. (Molecular weight of N₂ is 28 gm/mole) 10 marks
A body of constant heat capacity Cₚ and a temperature Tᵢ is put into contact with a reservoir at temperature Tƒ. Equilibrium between the body and the reservoir is established at constant pressure. Determine the total entropy change and prove that it is positive for either sign of [(Tƒ — Tᵢ)/Tƒ]. Consider |Tƒ — Tᵢ|/Tƒ < 1. 10 marks
Consider two point particles of charge q each, separated by a distance d, and travelling at non-relativistic velocity v⃗. If the line joining the two charges is perpendicular to v⃗, then write an expression for the magnetic force between the two particles, and illustrate the direction of the force on each particle. 10 marks
A cell of internal resistance 1 ohm, 1·5 volt e.m.f. and another cell of internal resistance 2 ohm, 2 volt e.m.f. are connected in parallel across the ends of an external resistance of 5 ohm. Find the current in each branch of the circuit. 10 marks
Consider the R-L-C circuit shown here. Calculate the Q-factor of the circuit. Does the circuit have a resonant frequency? Justify your answer : 10 marks
हिंदी में प्रश्न पढ़ें
मान लीजिए कि पृथ्वी का वायुमंडल 300 K के तापमान पर ऊष्मागतिक साम्य में शुद्ध नाइट्रोजन है। समुद्र-तल से ऊँचाई की गणना कीजिए जिस पर वायुमंडल का घनत्व उसके समुद्र-तल मान का आधा है। (N₂ का आण्विक भार 28 gm/mole है) (10 अंक)
नियत ऊष्मा धारिता Cₚ और तापमान Tᵢ का एक पिंड तापमान Tƒ पर एक भंडार (जलाशय) के संपर्क में आता है। अचल दाब पर पिंड और भंडार के बीच साम्यावस्था स्थापित होती है। कुल एन्ट्रॉपी परिवर्तन का निर्धारण कीजिए और सत्यापित कीजिए कि यह [(Tƒ — Tᵢ)/Tƒ] के किसी भी चिह्न के लिए धनात्मक है। मान लीजिए कि |Tƒ — Tᵢ|/Tƒ < 1 है। (10 अंक)
विचारिए कि दो बिंदु कण जिनमें प्रत्येक का आवेश q है, d दूरी से पृथक्कृत और अनापेक्षिकीय वेग v⃗ से गति कर रहे हैं। यदि दोनों आवेशों को मिलाने वाली रेखा v⃗ के लम्बवत् है, तो दोनों कणों के बीच चुंबकीय बल के लिए व्यंजक लिखिए और प्रत्येक कण पर बल की दिशा का वर्णन कीजिए। (10 अंक)
1·5 वोल्ट विद्युत वाहक बल तथा 1 ओम आंतरिक प्रतिरोध का एक सेल और 2 वोल्ट विद्युत वाहक बल तथा 2 ओम आंतरिक प्रतिरोध का दूसरा सेल 5 ओम के बाह्य प्रतिरोध के सिरों पर समांतर क्रम में जुड़े हुए हैं। परिपथ की प्रत्येक शाखा में धारा का मान ज्ञात कीजिए। (10 अंक)
चित्र में दिखाए गए R-L-C परिपथ पर विचार कीजिए। परिपथ के Q-गुणक की गणना कीजिए। क्या परिपथ में अनुनादी आवृत्ति होती है? उत्तर का औचित्य दीजिए : (10 अंक)
The figure this question refers to, in words
The question paper is a scan and the diagram did not survive as text. This is the figure as read from the original page — every component, value and label — so the question can be worked from the text below.
(e) A circuit diagram showing a DC voltage source labeled '4 V' connected in series with a switch labeled 'K'. The switch connects to a parallel circuit configuration. One branch of the parallel section contains an inductor labeled '1 mH' in series with a resistor labeled '4 Ohm'. The other branch contains a capacitor labeled '2 mF'. The bottom of the parallel branches connects back to the negative terminal of the voltage source.
What "Calculate" is asking you to do
Apply the standard formula or schedule to data the question has already supplied — a table of readings, cost records, a balance sheet — and produce the number. The method is rarely in doubt; the marks sit in the named intermediate quantities, each of which has to appear as a labelled line.
Structure that answers it
Data as given → formula or standard treatment, named → substitution → each intermediate, labelled → result with units
Where marks are lost
Omitting an intermediate the marking scheme pays for separately, or rounding at an intermediate line so the final figure drifts. In commerce and accountancy, any figure in a statement that no numbered working note supports is treated as unearned.
How this answer will be evaluated
Approach
(a) calculate: given > formula > substitution > result with units > interpretation | (b) derive: given > assumptions > stepwise derivation > result > check | (c) explain: definition/context > points in order > small example > short close | (d) calculate: given > formula > substitution > result with units > interpretation | (e) calculate: given > formula > substitution > result with units > interpretation Full marks: Rigorous derivation, correct units, clear diagrams, and physical interpretation for all parts.
Key points expected
- State barometric formula or derive from hydrostatic equilibrium
- Substitute T=300K, M=28g/mol, g=9.8m/s²
- Solve for h using ln(2) or log(2)
- Final answer in km with units
- Calculate ΔS_body = Cp ln(Tf/Ti)
- Calculate ΔS_res = -Cp(Tf-Ti)/Tf
- Sum to get ΔS_total expression
- Prove ΔS_total > 0 using Taylor expansion or inequality
Evaluation rubric
Each sub-part is marked on its own, against the marks and word limit printed on the paper.
- (a) Height where atmospheric density is half the sea-level value. 10 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- State barometric formula or derive from hydrostatic equilibrium
- Substitute T=300K, M=28g/mol, g=9.8m/s²
- Solve for h using ln(2) or log(2)
- Final answer in km with units
Loses marks
- Using wrong molecular weight (e.g. 14g/mol)
- Forgetting to convert grams to kg in M
Earns more
- Explicitly state assumption of isothermal atmosphere
- Show dimensional check of the exponent
Extra mark
- Mention scale height H = kT/mg
- (b) Total entropy change and proof of positivity for both signs. 10 marks
derive— given → assumptions → stepwise derivation → result → check
Must cover
- Calculate ΔS_body = Cp ln(Tf/Ti)
- Calculate ΔS_res = -Cp(Tf-Ti)/Tf
- Sum to get ΔS_total expression
- Prove ΔS_total > 0 using Taylor expansion or inequality
Loses marks
- Sign error in reservoir entropy change
- Failing to prove positivity for both signs
Earns more
- Explicitly handle case Ti > Tf and Ti < Tf
- Use the condition |Tf-Ti|/Tf < 1 in the proof
Extra mark
- Relate result to the Second Law of Thermodynamics
- (c) Expression for magnetic force and direction on each particle. 10 marks
explain— definition/context → points in order → small example → short close
Must cover
- Use Biot-Savart law or magnetic field of moving charge
- Apply Lorentz force F = qv × B
- Derive F ∝ v²/d (or similar) with correct vector direction
- Illustrate direction (attractive/repulsive) with a diagram
Loses marks
- Wrong direction of force (e.g. repulsive instead of attractive)
- Missing the v² dependence
Earns more
- Explicitly state the perpendicular geometry condition
- Mention non-relativistic approximation
Extra mark
- Compare magnitude with electrostatic force
- (d) Current in each branch of the parallel circuit. 10 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Apply Kirchhoff's Current Law (KCL) at the node
- Apply Kirchhoff's Voltage Law (KVL) for each loop
- Solve the system of linear equations for I1, I2, I3
- State currents with direction and units (A)
Loses marks
- Sign error in KVL equations
- Ignoring internal resistances
Earns more
- Draw the circuit diagram with labelled currents
- Check power balance (P_in = P_out)
Extra mark
- Calculate terminal voltage across the 5Ω resistor
- (e) Q-factor and justification for resonant frequency existence. 10 marks
calculate— given → formula → substitution → result with units → interpretation
Must cover
- Identify circuit as parallel RLC (from diagram)
- Calculate Q = R / (1/LC) or R * sqrt(C/L) for parallel
- Calculate resonant frequency ω0 = 1/sqrt(LC)
- Justify existence based on R, L, C values
Loses marks
- Using series RLC formula for Q
- Failing to justify the resonant frequency claim
Earns more
- Show the formula for Q in parallel RLC
- Calculate numerical value of ω0 in rad/s
Extra mark
- Mention bandwidth Δω = ω0/Q
Model answer coming soon
Every evaluation on this site is marked against a verified model answer. This question's answer is still being written; evaluation opens the moment it lands.
More from Physics 2022 Paper I
- Q2 Consider two frames of reference S and S' having a common origin O. The frame S' is rotat…
- Q3 (a) A homogeneous right triangular pyramid with the base side a and height 3a/2 is shown…
- Q4 (a) Consider the diagram below with a water flow rate Q. Derive the expression for Q in t…
- Q5 (a) Assume that the Earth's atmosphere is pure nitrogen in thermodynamic equilibrium at a…
- Q6 (a) Write down Maxwell's equations in a non-conducting medium with constant permeability…
- Q7 (a) A metal guitar string with a length of 70 cm vibrates at its fundamental frequency of…
- Q8 (a) In a partially conducting medium, εᵣ = 18.5, μᵣ = 800 and σ = 1 S m⁻¹. Find α, β, η a…