🔥 Thermodynamics – Stage 1
Page 8 : Heat Capacity & Mayer’s Relation (JEE Core)
Heat Capacity tells how much heat is required to raise temperature.
1️⃣ Heat Capacity (General Definition)
C = ΔQ / ΔT
• Depends on process
• Depends on constraints (P or V constant)
• Depends on constraints (P or V constant)
2️⃣ Heat Capacity at Constant Volume (Cv)
Volume remains constant → No work done
Cv = (ΔQ / ΔT)V
From First Law:
ΔQ = ΔU
Therefore,
Cv = (∂U / ∂T)
ΔQ = ΔU
Therefore,
Cv = (∂U / ∂T)
⚠ At constant volume → All heat increases internal energy
3️⃣ Heat Capacity at Constant Pressure (Cp)
Pressure remains constant → Work is done
Cp = (ΔQ / ΔT)P
ΔQ = ΔU + PΔV
⚠ Heat supplied increases internal energy + does work
4️⃣ Relation Between Cp and Cv
For all gases:
Cp > Cv
Reason: Extra heat is used to perform work at constant pressure
5️⃣ Mayer’s Relation (Most Important)
Cp − Cv = R
Valid only for ideal gases
R → Universal gas constant
6️⃣ Degrees of Freedom (f)
Energy storage modes of gas molecules
Cv = (f/2)R
Cp = ((f + 2)/2)R
Cp = ((f + 2)/2)R
| Gas | f | Cv | Cp |
|---|---|---|---|
| Monoatomic | 3 | 3R/2 | 5R/2 |
| Diatomic | 5 | 5R/2 | 7R/2 |
| Polyatomic | 6 | 3R | 4R |
7️⃣ JEE-Trap Notes
⚠ Mayer’s relation fails for real gases
⚠ Cp, Cv are process dependent
⚠ Use degrees of freedom carefully
⚠ Cp, Cv are process dependent
⚠ Use degrees of freedom carefully
👉 Next Page:
Page 9 – Adiabatic Process & Poisson’s Equations
Page 9 – Adiabatic Process & Poisson’s Equations
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