Heat & Thermodynamics
Practice JEE Main Heat & Thermodynamics PYQs online. First law of thermodynamics, Carnot engine efficiency η = 1 - T₂/T₁, adiabatic processes & solutions.
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🎯 High-Yield Syllabus Breakdown
These high-frequency concepts account for over 90% of all questions asked in Heat & Thermodynamics:
- Thermal Expansion, Calorimetry & Heat Transfer (Conduction, Convection, Radiation)
- First Law of Thermodynamics: ΔQ = ΔU + W (where ΔU = n C_v ΔT)
- Thermodynamic Processes: Isothermal (W = nRT ln(V₂/V₁)), Adiabatic (P V^γ = const)
- Carnot Heat Engine & Refrigerator: η = 1 - T_sink / T_source = W / Q_in
- Kinetic Theory of Gases (KTG) & Degrees of Freedom
⚡ Essential Formulas & Speed Shortcuts
Formulas and time-saving shortcuts to solve Thermodynamics questions in under 45 seconds:
Carnot Efficiency: η = 1 - T₂ / T₁ (Temperatures must ALWAYS be in Kelvin).
Adiabatic Work: W = (P₁ V₁ - P₂ V₂) / (γ - 1) = n R (T₁ - T₂) / (γ - 1).
Molar heat capacity ratio: γ = C_p / C_v = 1 + 2/f (Monoatomic f=3, γ=5/3; Diatomic f=5, γ=7/5).
📖 Sample Solved Exam Questions
Preview authentic questions from this chapter with full step-by-step solutions:
💡 View Step-by-Step Solution & Answer
Correct Answer: 500 J
- Step 1: Carnot efficiency formula: η = 1 - T_C / T_H.
- Step 2: Substitute temperatures: η = 1 - 300 / 600 = 1 - 0.5 = 0.5 (50%).
- Step 3: Work output relation: W = η · Q_in.
- Step 4: W = 0.5 × 1000 J = 500 J.
⚡ Speed Tip: Carnot Efficiency: η = (600 - 300)/600 = 50%. W = 0.5 × 1000 = 500 J.
💡 View Step-by-Step Solution & Answer
Correct Answer: 3/2
- Step 1: Standard adiabatic relation in terms of P and T: P^(1 - γ) · T^γ = constant ⇒ P ∝ T^(γ / (γ - 1)).
- Step 2: Given relation: P ∝ T³.
- Step 3: Equate exponents: γ / (γ - 1) = 3.
- Step 4: Solve for γ: γ = 3(γ - 1) = 3γ - 3 ⇒ 2γ = 3 ⇒ γ = 3/2.
⚡ Speed Tip: Adiabatic P-T relation: γ / (γ - 1) = 3 ⇒ γ = 3/2 = 1.5.
💡 View Step-by-Step Solution & Answer
Correct Answer: 498.6 J
- Step 1: For a monoatomic gas, molar heat capacity at constant volume is C_v = (3/2) R.
- Step 2: Change in internal energy is always ΔU = n C_v ΔT (regardless of the process).
- Step 3: Substitute given values: ΔU = (1 mol) × (3/2 × 8.31 J/(mol·K)) × (40 K).
- Step 4: ΔU = 1.5 × 8.31 × 40 = 60 × 8.31 = 498.6 J.
⚡ Speed Tip: Internal Energy: ΔU = n C_v ΔT = (3/2) R (40) = 60 R = 60 × 8.31 = 498.6 J.
❓ Frequently Asked Questions (FAQs)
Can Carnot efficiency ever be 100%?
No, efficiency can only reach 100% if the sink temperature is at absolute zero (0 K), which is physically impossible.