First Law of Thermodynamics
The energy of an isolated system is constant ⚖️. For any change:
\[ \Delta U = q + w \]Where:
• \(\Delta U\) = change in internal energy
• \(q\) = heat transferred
• \(w\) = work done on the system
Key ideas:
• \(\Delta U\) depends only on initial & final states
• \(q\) and \(w\) depend on how the change happens
• If no heat/work exchange: \(\Delta U = 0\)
Special Cases
- 🔒 Adiabatic wall (no heat exchange): \(\Delta U = w\)
- 🔥 Constant volume: \(\Delta U = q_v\)
- 💨 Free expansion (vacuum): \(w = 0\), \(q = 0\), \(\Delta U = 0\)
Pressure-Volume Work
For gas expansion/compression:
\[ w = -p_{ex} \Delta V \]Irreversible process (single step):
Work = shaded area on pV graph
\[
w = -p_{ex} (V_f – V_i)
\]
Reversible process (infinite slow steps):
\[
w_{\text{rev}} = -\int_{V_i}^{V_f} p_{\text{in}} dV
\]
For ideal gas at constant T:
\[
w_{\text{rev}} = -2.303 nRT \log\frac{V_f}{V_i}
\]
Enthalpy (H)
New state function for constant-pressure processes: 🌡️
\[ H = U + pV \]• Heat at constant pressure: \(\Delta H = q_p\)
• Relation to \(\Delta U\): \(\Delta H = \Delta U + p\Delta V\)
• For gases: \(\Delta H = \Delta U + \Delta n_g RT\)
(where \(\Delta n_g\) = moles gas products – reactants)
Exothermic: \(\Delta H < 0\) (releases heat) 🔥
Endothermic: \(\Delta H > 0\) (absorbs heat) ❄️
Example
Vaporizing 1 mol water at 100°C:
\(\Delta H = 41\) kJ/mol
\(\Delta U = \Delta H – \Delta n_g RT = 41 – (1)(8.3)(373)/1000 = 37.9\) kJ/mol
Heat Capacity
Heat needed to raise temperature: 🌡️➡️🌡️
\[ q = C \Delta T \]- \(C_v\) = heat capacity at constant volume → \(\Delta U = C_v \Delta T\)
- \(C_p\) = heat capacity at constant pressure → \(\Delta H = C_p \Delta T\)
For ideal gases:
\[
C_p – C_v = R
\]
Calorimetry
Measuring energy changes: 🔍
Constant volume (bomb calorimeter):
• Sealed steel vessel in water bath
• Measures \(q_v = \Delta U\)
• No work done (\(w = 0\))
Constant pressure:
• Open container
• Measures \(q_p = \Delta H\)
NEET Super Focus 🔥
- First Law applications: Calculate \(\Delta U\), \(q\), \(w\) for different processes (isothermal, adiabatic, free expansion)
- Work calculations: \(w = -p_{ex}\Delta V\) for irreversible vs. reversible processes
- \(\Delta H\) vs. \(\Delta U\): Use \(\Delta H = \Delta U + \Delta n_g RT\) for reactions involving gases
- Heat capacity: \(C_p – C_v = R\) for ideal gases
- Calorimetry: Bomb calorimeter measures \(\Delta U\) at constant volume
