Specific Heat Capacity 🌡️

Imagine heating some water on a stove. The hotter it gets, the faster the bubbles dance! 🔥 Experiments show that the heat needed to warm anything depends on three things: mass (m), temperature rise (ΔT), and the kind of stuff you’re heating. :contentReference[oaicite:0]{index=0}

Heat Capacity ( S )

\( S = \dfrac{\Delta Q}{\Delta T} \)    (10.10) :contentReference[oaicite:1]{index=1}

  • Q = heat added or removed
  • Units: J K−1

Specific Heat Capacity ( s )

\( s = \dfrac{1}{m}\,S = \dfrac{\Delta Q}{m\,\Delta T} \)    (10.11) :contentReference[oaicite:2]{index=2}

  • Heat per kilogram for a 1 K jump.
  • Units: J kg−1 K−1.
  • Every substance has its own s.

Molar Specific Heat Capacity ( C )

\( C = \dfrac{\Delta Q}{\mu\,\Delta T} \)    (10.12) :contentReference[oaicite:3]{index=3}

  • Per mole instead of per kilogram.
  • Units: J mol−1 K−1.
  • For gases we meet two stars: Cp (constant pressure) and Cv (constant volume). :contentReference[oaicite:4]{index=4}

Typical Values 📝

Specific heat capacity at room temperature

SubstanceJ kg−1 K−1
Water4186.0
Aluminium900.0
Carbon506.5
Copper386.4
Glass840
Iron450
Lead127.7
Silver236.1
Tungsten134.4
Kerosene2118
Edible oil1965
Ice2060
Mercury140

Water tops the chart, so it’s perfect for car radiators 🚗💧 and hot-water bags. :contentReference[oaicite:5]{index=5}

Molar specific heats of common gases

GasCp (J mol−1 K−1)Cv (J mol−1 K−1)
He20.812.5
H228.820.4
N229.120.8
O229.421.1
CO237.028.5
:contentReference[oaicite:6]{index=6}

Why Location Matters 🌊🏜️

Coastal water warms up slowly and cools down slowly, giving comfy sea breezes. Dry desert sand—with a much smaller s—heats fast by day and chills fast by night. :contentReference[oaicite:7]{index=7}

Sample Problem ⚡

Drop a 0.047 kg aluminium sphere at 100 °C into 0.25 kg of 20 °C water sitting in a 0.14 kg copper cup. Everything settles at 23 °C. Set up the heat-balance equation:

\( m_{\text{Al}}\,s_{\text{Al}}\,(100-23) = m_{\text{Cu}}\,s_{\text{Cu}}\,(23-20) + m_{\text{w}}\,s_{\text{w}}\,(23-20) \)

Plugging the numbers gives \( s_{\text{Al}} \approx 900\;\text{J kg}^{-1}\text{K}^{-1} \) 🎉—exactly what the table said! :contentReference[oaicite:8]{index=8}

Important Concepts for NEET 🎯

  1. The magic triangle \( Q = m\,s\,\Delta T \) (know how to shuffle it for any unknown).
  2. Cp vs. Cv—pick the right one when pressure or volume stays steady.
  3. Heat capacity (S) and specific heat capacity (s) are buddies: S = m s.
  4. Water’s giant specific heat capacity and the cool tricks it plays in climate and cooling systems.
  5. Calorimetry rule: heat lost = heat gained—your gateway to finding unknown heats in the lab.