Chapter 1: Thermal Physics — MCQs (59 Solved)
Overview
Ye MCQs do sections mein hain: Section A (Q1–8) textbook ke official exercise se hain, aur Section B (Q9–59) extra practice ke liye hain. Sab MCQs unhi concepts ko test karte hain jo humne pehle exercise, long questions, aur short questions mein cover kiye — bas yahan quick recall aur calculation speed check hoti hai.
Group 1: Ideal Gas Behaviour aur rms Speed Calculations (Q1–5, 27–31)
Ye sab questions vrms ke formulas ghumate hain:
vrms=3RTM=3Pρv_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3P}{\rho}}
- Q1: Gas high temperature aur low pressure par ideal behave karti hai (molecules door aur tez hote hain)
- Q2, Q3, Q29, Q30: Sab isi rule par based hain: vrms ∝ √(T/M). Jab T ya M badle, seedha ratio nikal kar naya vrms calculate karo (jaise T half aur M double → vrms half; T char guna → vrms 2 guna; m double → vrms 1/√2 guna)
- Q4: vrms ∝ 1/√M, isliye O₂ aur H₂ ka ratio √(M(H₂)/M(O₂)) se nikla → 1:4
- Q5, Q27, Q28: Formula P=(1/3)ρv²rms ya iska rearranged form vrms=√(3P/ρ) use hota hai — pressure aur density diye jaate hain, seedha substitute karo
- Q31: Boyle’s law ka application — constant T par volume half karne se pressure double ho jata hai
Yaad rakhne wala trick: Jahan bhi T ya M mein tabdeeli ho, seedha √(T/M) ka ratio nikalo — poori calculation ki zaroorat nahi.
Group 2: Kinetic Theory Ki Bunyadi Assumptions (Q6, 15–20)
- Q6: Kinetic theory collisions ko elastic maanti hai, inelastic nahi — ye ek common trap hai
- Q15: Molecules ko point-like aur door door treat kiya jata hai (unka apna volume negligible hai)
- Q16: Wall ke saath collisions perfectly elastic maane jate hain
- Q17, Q19: Intermolecular forces negligible maani jaati hain (sirf collision ke waqt) — “strong attraction” wala option hamesha galat hota hai
- Q18: Average KE sirf temperature par depend karti hai
- Q20: Chhote se gas cube mein bhi molecules ki tadaad 10¹⁹ ke order mein hoti hai — bohot bara number
Group 3: Pressure Ki Derivation Se Related (Q21–27)
Ye questions PV=(1/3)Nm⟨v²⟩ derivation ke individual steps test karte hain:
- Q21: Pressure molecules ke walls se collision ki wajah se paida hoti hai
- Q22: Elastic collision mein momentum change = 2mv (velocity reverse hone ki wajah se)
- Q23: Time between collisions = 2L/v (distance/speed)
- Q24: Formula PV=(1/3)Nm⟨v²⟩ macroscopic pressure/volume ko microscopic mass/speed se jorta hai
- Q25: rms speed ki definition: squared velocities ka average, phir square root
- Q26: 3D random motion ki wajah se har axis (x,y,z) total mean square speed ka 1/3 hisaab leti hai
Sabak: Ye sab derivation ke wahi steps hain jo humne Long Questions mein detail se dekhe the — MCQs mein wahi steps individually poochay jaate hain.
Group 4: Temperature Aur Kinetic Energy (Q32–39)
- Q32: Constant volume par temperature barhane se molecular speed aur pressure dono barh jaate hain
- Q33, Q34: Average KE ka formula: (3/2)kT — sirf temperature par proportional
- Q35: Room temperature (300K) par kBT ≈ 4.14×10⁻²¹ J — ye numerical substitution hai
- Q36: 1 eV = 1.6×10⁻¹⁹ J — ye ek standard conversion factor hai, yaad rakhna zaroori hai
- Q37: T double hone se average KE bhi double hoti hai (seedha proportional hai)
- Q38: Alag alag gases (jaise O₂ aur He) ki average KE barabar hoti hai agar temperature same ho — mass ka farq nahi parta
- Q39: Density double, vrms same rahe to pressure bhi double ho jaati hai (P∝ρ)
Group 5: Boltzmann Distribution Aur Statistical Physics (Q40–46)
- Q40: Kinetic theory ne statistical mechanics ki bunyad rakhi
- Q41, Q42: Boltzmann law particles ki probability distribution batata hai energy states mein — lower energy states mein zyada particles hote hain
- Q43: Boltzmann factor ki shakal: e^(−ΔE/kT) — negative exponent yaad rakho, positive nahi
- Q44, Q45, Q46: Statistical physics bohot zyada particles ke liye useful hai, aur ye probability theory par based hai
Yaad rakhne ka tareeqa: Boltzmann factor mein hamesha negative sign hota hai kyunke jitni energy zyada, utni population kam hoti jaati hai.
Group 6: Stars Ki Stability (Hydrostatic Equilibrium) (Q47–51)
- Q47, Q48: Star tab stable hota hai jab gravity aur internal pressure exactly balance hon — formula: ΔP/Δr = −GMᵣρᵣ/r²
- Q49: Gravity zyada ho to star contract hota hai, core ka temperature barhta hai
- Q50: Pressure zyada ho to star expand hota hai
- Q51: Nuclear fusion tab shuru hota hai jab core ka temperature itna barh jaye ke hydrogen fuse hona shuru ho jaye
Group 7: Stellar Evolution Ka Anjaam (Q52–59)
- Q52: Sun se ~10 guna bare stars supernova ke baad neutron star ya black hole bante hain
- Q53: Chhote/medium stars white dwarf bante hain (aur planetary nebula chhor jate hain)
- Q54: Neutron stars itne dense isliye hote hain kyunke matter degenerate gas ki tarah gravity ke under compress ho jata hai
- Q55: Pulsar = tezi se ghumta hua neutron star jo radiation ke beams nikalta hai
- Q56: Sun abhi main sequence stage mein hai
- Q57 (Sun ki life ka sahi order): Nebula→Protostar→Main Sequence→Red Giant→Planetary Nebula→White Dwarf\text{Nebula} \to \text{Protostar} \to \text{Main Sequence} \to \text{Red Giant} \to \text{Planetary Nebula} \to \text{White Dwarf} Ye sequence yaad rakhna zaroori hai
- Q58: Parsec ek bare astronomical distances naapne ki unit hai
- Q59: Star ki zindagi bhar ki energy ka main source hydrogen ka helium mein nuclear fusion hai
Sabse Zaroori Formulas Jo In MCQs Mein Baar Baar Use Hue:
| Formula | Kahan Use Hota Hai |
|---|---|
| vrms = √(3RT/M) = √(3P/ρ) | Speed calculations |
| PV = (1/3)Nm⟨v²⟩ | Pressure derivation |
| ⟨K.E.⟩ = (3/2)kT | Temperature-energy relation |
| N₂/N₁ = e^(−ΔE/kT) | Boltzmann distribution |
| ΔP/Δr = −GMᵣρᵣ/r² | Star stability |
Exam Tip: In MCQs mein zyada tar sawalat proportion (∝) ka concept test karte hain — jaise vrms∝√T, ya KE∝T. Agar ye relations achi tarah yaad hon, to bina lambi calculation ke bhi jaldi sahi option choose kiya ja sakta hai.