QCC Notes
CLASS 11 · PHYSICSJEE MAIN × NEETहिंदी
§ 10.3NCERT Class 11 · Physics · Chapter 10

Specific Heat Capacity & Calorimetry – Complete Notes

QCC Notes · Class 11 Physics NCERT-aligned Updated 26 Sep 2026 5 min read

When heat energy is supplied to a substance, it either raises its temperature (sensible heat) or causes a phase change without altering its temperature (latent heat). Calorimetry (measurement of heat) provides the quantitative framework for computing temperature equilibration and phase transitions.

1. Heat Capacity & Specific Heat Capacity

Heat Capacity (S)

The amount of heat required to raise the temperature of the entire body by 1 °C (or 1 K):

S = ΔQ / ΔT
SI Unit: J K−1

Heat capacity is an extensive property; it depends on the mass and nature of the body.

Specific Heat Capacity (s or c)

The heat required to raise the temperature of unit mass of a substance by 1 °C (or 1 K):

c = ΔQ / (m ΔT) ⇒ ΔQ = m c ΔT
SI Unit: J kg−1 K−1

Specific heat is an intensive property characteristic of the substance.

Unique High Specific Heat of Water

Water has an exceptionally high specific heat capacity: cw = 4186 J kg−1 K−1 ≈ 1.0 cal g−1 °C−1. In contrast, metals have much lower values (e.g., copper: 386 J kg−1 K−1, lead: 128 J kg−1 K−1). Key environmental consequences:

  • Maritime Climate: Oceans warm up and cool down much slower than land, moderating coastal climate extremes.
  • Automobile Coolant: Circulating water absorbs huge quantities of engine heat with minimal temperature rise.
  • Biological Thermal Buffer: The high water content in living tissues protects organisms from lethal thermal shocks.

2. Molar Heat Capacities of Gases

For gases, the heat absorbed depends strongly on the thermodynamic conditions during heating:

  • Molar Heat Capacity at Constant Volume (Cv): Cv = (1/n) (ΔQ/ΔT)v = (dU/dT). For ideal gas: Cv = (f/2) R (where f is degrees of freedom).
  • Molar Heat Capacity at Constant Pressure (Cp): Cp = (1/n) (ΔQ/ΔT)p = Cv + R.
  • Mayer's Relation: Cp − Cv = R (in molar units) or cp − cv = r = R/M (in mass specific units).
  • Adiabatic Index: γ = Cp / Cv = 1 + 2/f.

3. The Principle of Calorimetry (Method of Mixtures)

A calorimeter is a copper or aluminum vessel enclosed within a wooden box insulated by glass wool to prevent radiative, conductive, and convective heat losses. According to the conservation of thermal energy in an isolated system:

Heat Lost by Hotter Bodies = Heat Gained by Colder Bodies
Water Equivalent (W):
The mass of water which absorbs or releases the exact same amount of heat as the calorimeter for an identical temperature change:
W = mcal × ccal / cw (in grams, if ccal is in cal g−1 °C−1).
Total heat gained by calorimeter and liquid of mass m1: ΔQ = (m1 c1 + W cw) (Teq − T1).

4. Changes of State & Latent Heat

Matter undergoes transitions between solid, liquid, and gas phases. During a phase transition, temperature remains strictly constant while heat is absorbed or released:

Phase Change Heat Formula:
ΔQ = m L

where L is the Latent Heat of the transition. SI unit: J kg−1.

Latent Heat of Fusion (Lf)

Heat required to convert 1 kg of solid into liquid at its melting point:

  • For ice at 0 °C: Lf = 3.33 × 105 J kg−1 ≈ 80 cal g−1.
  • Represents energy consumed to break rigid crystalline hydrogen bonds without increasing kinetic energy.

Latent Heat of Vaporisation (Lv)

Heat required to convert 1 kg of liquid into vapour at its boiling point:

  • For water at 100 °C: Lv = 2.26 × 106 J kg−1 ≈ 540 cal g−1.
  • Lv is ~ 7 times greater than Lf because molecules are completely separated against cohesive forces and work is done against atmospheric pressure.

5. Effect of Pressure on Phase Transitions & Regelation

  • Melting Point & Pressure: For substances that contract on melting (like ice), increasing pressure lowers the melting point. For substances that expand on melting (like wax, paraffin), increasing pressure raises the melting point.
  • Regelation: The phenomenon where ice melts under increased pressure and refreezes when the pressure is released (demonstrated by a weighted wire cutting through an ice block without cleaving it). Ice skating is enabled because high pressure under the sharp skate blade melts a microscopic water lubricant film.
  • Boiling Point & Pressure: Boiling point increases with increasing external pressure. In a pressure cooker, steam pressure reaches ~ 2 atm, raising the boiling point of water to ~ 120 °C, cooking food much faster. Conversely, at high altitudes (low atmospheric pressure), water boils below 100 °C, making cooking difficult.
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