Understanding Heat and Specific Heat 🔥

Specific heat (\(c\)) is the heat needed to raise 1 gram of a substance by 1°C (or 1 K). To calculate heat (\(q\)) for any sample:

\[q = c \times m \times \Delta T\]

or simply \(q = C \Delta T\), where \(C\) is total heat capacity.

Heat Capacity at Constant Volume vs. Pressure 🔧

  • At constant volume: Heat capacity = \(C_v\), and \(q_v = \Delta U\).
  • At constant pressure: Heat capacity = \(C_p\), and \(q_p = \Delta H\).

For an ideal gas, they’re related by:

\[C_p – C_v = R\]

where \(R\) is the gas constant (8.314 J/mol·K).

Measuring ΔU and ΔH: Calorimetry 🌡️

(a) ΔU Measurements (Constant Volume)

Use a bomb calorimeter (steel vessel in water bath):

  • No volume change → \(\Delta V = 0\) → \(\Delta U = q_v\).
  • Reaction heat warms the water. Measure \(\Delta T\) and use:

\[q_v = C_v \Delta T\]

where \(C_v\) = heat capacity of the calorimeter.

(b) ΔH Measurements (Constant Pressure)

Use a simple calorimeter (e.g., polystyrene cup):

  • Heat change at constant pressure = \(q_p = \Delta H\).
  • Exothermic reaction → heat released → \(\Delta H < 0\).
  • Endothermic reaction → heat absorbed → \(\Delta H > 0\).

Example Problem 💡

Problem: Burning 1g graphite in a bomb calorimeter (\(C_v = 20.7 \text{ kJ/K}\)) raises temperature from 298K to 299K. Find \(\Delta H\) at 298K.

Solution:

  1. Heat released by reaction: \(q_v = -C_v \Delta T = -20.7 \times (299-298) = -20.7 \text{ kJ}\).
  2. For 1g graphite, \(\Delta U = q_v = -20.7 \text{ kJ}\).
  3. For 1 mol (12g): \(\Delta U = 12 \times (-20.7) = -248.4 \text{ kJ/mol}\).
  4. Since \(\Delta n_g = 0\) (no gas moles change), \(\Delta H = \Delta U = -248.4 \text{ kJ/mol}\).

Reaction Enthalpy (ΔH) ⚗️

For any reaction: \(\text{Reactants} \rightarrow \text{Products}\),

\[\Delta H = (\text{Sum of enthalpies of products}) – (\text{Sum of enthalpies of reactants})\]

or more precisely:

\[\Delta H = \sum a_i H_{\text{products}} – \sum b_i H_{\text{reactants}}}\]

where \(a_i\), \(b_i\) are stoichiometric coefficients.

Important Concepts for NEET 🎯

  • 🔥 \(C_p – C_v = R\) for ideal gases (always asked!).
  • 🧪 Bomb calorimeter measures \(\Delta U\) at constant volume.
  • ⚖️ Constant-pressure calorimetry gives \(\Delta H\) (and sign determines exo/endo-thermic).
  • 📐 \(\Delta H = \Delta U\) when \(\Delta n_g = 0\) (e.g., graphite combustion problem).
  • ➖ ΔH calculation from calorimetry data (practice the formula \(q = C \Delta T\)!).

Keep practicing calorimetry problems—they’re easy marks in NEET! 💯