🔥 Thermodynamics – Stage 1

Page 4 : Specific Heat Capacities & Mayer’s Relation

Core Idea:
Specific heat tells us how much heat is required to raise the temperature of a system.

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1️⃣ Heat Capacity & Specific Heat

Heat Capacity (C):
Amount of heat required to raise temperature of a body by 1 K.

Specific Heat (c):
Heat required to raise temperature of unit mass by 1 K.

⚠ Specific heat depends on the process (path dependent)

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2️⃣ Two Important Specific Heats of Gas

(a) Specific Heat at Constant Volume (C_v)
• Volume remains constant
• No work is done (W = 0)
• Heat supplied increases internal energy only

Mathematically:
dQ = n C_v dT

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(b) Specific Heat at Constant Pressure (C_p)
• Pressure remains constant
• Gas expands → work is done
• Heat increases both internal energy + work

Mathematically:
dQ = n C_p dT

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3️⃣ Why is C_p > C_v?

At constant pressure, extra heat is needed to perform expansion work.

Hence:
C_p > C_v

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4️⃣ Mayer’s Relation (VERY IMPORTANT)

C_p − C_v = R

This relation is valid only for ideal gases.

❌ Not valid for real gases

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5️⃣ Ratio of Specific Heats (γ)

γ (Gamma) = C_p / C_v

Typical values:
Monoatomic gas → γ = 5/3
Diatomic gas → γ = 7/5

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6️⃣ JEE Favourite Traps

• C_p, C_v are not state functions
• Mayer’s relation holds only for ideal gas
• γ decides adiabatic behavior
• C_p − C_v ≠ temperature dependent

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7️⃣ Typical JEE Applications

✔ Adiabatic equations
✔ Speed of sound in gas
✔ Engine efficiency
✔ Conceptual MCQs

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👉 Next Page:
Page 5 – Thermodynamic Processes (Isothermal, Adiabatic, Isobaric, Isochoric)

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🔥 Thermodynamics – Objective Final Revision

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
Set 43
Set 44
Set 45
Set 46
Set 47
Set 48
Set 49
Set 50
Set 51
Set 52
Set 53
Set 54
Set 55
Set 56
Set 57
Set 59

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