🌡️ Thermodynamics – Stage 2

Page 4 : Heat Capacities, Cp vs Cv & Graph Traps

Heat capacity questions are silent killers in JEE Advanced. Concepts are simple — traps are deadly.

1️⃣ Heat Capacity – Fundamental Definition

Heat Capacity (C) = Heat required to raise temperature by 1 K

Specific Heat: per unit mass
Molar Heat: per mole

2️⃣ Cp and Cv – Core Difference

Cv → Heat capacity at constant volume
Cp → Heat capacity at constant pressure

👉 At constant pressure, gas does extra work
👉 Therefore Cp > Cv

3️⃣ Mayer’s Relation (Extremely Important)

Cp − Cv = R (for ideal gas)

✔ Valid only for ideal gases
❌ Not valid for solids or liquids

4️⃣ Heat Supplied in Different Processes

Isochoric: Q = nCvΔT
Isobaric: Q = nCpΔT
Isothermal: Q = W
Adiabatic: Q = 0

⚠ Students often mix Cp & Cv blindly

5️⃣ γ (Gamma) – Heat Capacity Ratio

γ = Cp / Cv

Monatomic gas → γ = 5/3
Diatomic gas → γ = 7/5

6️⃣ Graphical Traps (Very High Yield)

Area under curve represents:

P–V graph → Work
T–S graph → Heat

❌ Area under T–V or P–T has NO direct meaning

7️⃣ Cp & Cv from Graphs

If slope of Q vs T is given:

At constant V → slope = nCv
At constant P → slope = nCp

8️⃣ JEE Advanced Thinking Rule

Always ask:

Is volume fixed or pressure fixed?
Is gas ideal?
Is work involved?

✅ Stage 2 – Page 4 Complete
👉 Next: Stage 2 – Page 5 : Adiabatic Process & Poisson’s Equations

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Thermodynamics – Set 1
Set 2
Set 3
Set 4
Set 5
Set 6
Set 7
Set 8
Set 9
Set 10
Set 11
Set 12
Set 13
Set 14
Set 15
Set 16
Set 17
Set 18
Set 19
Set 20
Set 21
Set 22
Set 23
Set 24
Set 25
Set 26
Set 27
Set 28
Set 29
Set 30
Set 31
Set 32
Set 33
Set 34
Set 35
Set 36
Set 37
Set 38
Set 39
Set 40
Set 41
Set 42
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