## 6.3 HEAT AND TEMPERATURE This section explores the fundamental concepts of heat and temperature, their relationship, and how heat changes in chemical reactions are measured using calorimetry. ## Heat as a Form of Energy **Heat** is a form of energy that arises from the movement (kinetic energy) of molecules within a substance. When a body absorbs heat, it becomes hotter; when it releases heat, it becomes colder. The **Law of Conservation of Energy** states that energy cannot be created or destroyed, only converted from one form to another. Heat is one of these forms, alongside light, mechanical, chemical, and nuclear energy. **Example**: Boiling water in a pot causes the lid to jump. This demonstrates the conversion of heat energy from the stove into mechanical energy that moves the lid. The SI unit for heat is the **Joule (J)**. It is also commonly measured in **calories (cal)**. ## Heat vs. Temperature While related, heat and temperature are distinct concepts. Temperature is considered an intensive property because it does not depend on the amount of matter present. | Feature | **Heat (q)** | **Temperature (T)** | |---------|--------------|---------------------| | **Definition** | The *total* energy produced by the movement of all molecules in a substance. | A measure of the *average* kinetic energy of the molecules in a substance. It describes the intensity of heat (hotness or coldness). | | **Depends On** | Particle speed, particle size, and **number of particles**. | Particle speed (average kinetic energy). | | **Units** | Joules (J), calories (cal) | Kelvin (K), Celsius (°C), Fahrenheit (°F) | **Example**: A large jar and a small glass both filled with water at the same temperature. The water in both has the same average kinetic energy (same temperature), but the jar contains more water molecules, so it possesses more total heat energy. ## Heat Capacity and Specific Heat Capacity The amount of heat absorbed ($q$) by a substance is directly proportional to its temperature change ($\Delta T$). $$q \propto \Delta T$$ $$q = \text{Heat Capacity} \times \Delta T$$ * **Heat Capacity (C)**: The amount of heat required to raise the temperature of a given amount of a substance by 1 Kelvin. $$\text{Heat Capacity} = \frac{q}{\Delta T}$$ * Units: Joules per Kelvin ($J\,K^{-1}$). * **Specific Heat Capacity (c)**: The amount of heat required to raise the temperature of **one gram** of a substance by 1 Kelvin. $$c = \frac{q}{m \times \Delta T}$$ * This leads to the fundamental equation for heat calculation: $$q = m \times c \times \Delta T$$ * Where: * $q$ = heat absorbed or released (J) * $m$ = mass of the substance (g) * $c$ = specific heat capacity ($J\,g^{-1}\,K^{-1}$) * $\Delta T$ = change in temperature (K or °C) * **Molar Heat Capacity**: The heat capacity per mole of a substance ($J\,mol^{-1}\,K^{-1}$). **Example**: * Specific heat capacity of Copper (Cu) = $0.387\,J\,g^{-1}\,K^{-1}$ * Molar mass of Cu = $63.54\,g\,mol^{-1}$ * Molar heat capacity of Cu = $0.387 \, J\,g^{-1}\,K^{-1} \times 63.54 \, g\,mol^{-1} = 24.59 \, J\,mol^{-1}\,K^{-1}$ ## Measurement of Heat of Reaction (Calorimetry) A **calorimeter** is a device used to measure the heat flow associated with a chemical or physical process. ### Constant Pressure Calorimeter This type of calorimeter measures heat changes at a constant atmospheric pressure. A simple and common version is the **coffee cup calorimeter**. It consists of a thermally insulated container (like a Styrofoam cup), a lid, a thermometer, and a stirrer. The heat absorbed or released by the reaction ($q_{rxn}$) is equal in magnitude but opposite in sign to the heat absorbed or released by the solution ($q_{soln}$). $$q_{rxn} = -q_{soln}$$ The heat change of the solution is calculated using: $$q_{soln} = m \times c \times \Delta T$$ Where $m$ is the total mass of the solution and $c$ is the specific heat of the solution (often assumed to be that of water). ## Worked Examples ### Example 6.4: Calculating Heat of Neutralization When $50\,cm^3$ of $1.0\,M$ NaOH neutralizes $50\,cm^3$ of $1.0\,M$ HCl at $25^\circ C$, the temperature rises to $31.9^\circ C$. Calculate the heat of neutralization. (Specific heat of water = $4.2\,J\,g^{-1}\,K^{-1}$. Density of water = $1\,g\,cm^{-3}$) **Solution:** 1. **Write the given values and calculate initial parameters:** * Volume of NaOH = $50\,cm^3$ * Volume of HCl = $50\,cm^3$ * Total Volume = $50\,cm^3 + 50\,cm^3 = 100\,cm^3$ * Density of solution (assumed to be water) = $1\,g\,cm^{-3}$ * Specific heat capacity ($c$) = $4.2\,J\,g^{-1}\,K^{-1}$ * Initial Temperature ($T_i$) = $25^\circ C$ * Final Temperature ($T_f$) = $31.9^\circ C$ 2. **Calculate the mass (m) of the reaction mixture:** $$m = \text{Total Volume} \times \text{Density}$$ $$m = 100\,cm^3 \times 1\,g\,cm^{-3} = 100\,g$$ 3. **Calculate the change in temperature ($\Delta T$):** $$\Delta T = T_f - T_i = 31.9^\circ C - 25^\circ C = 6.9^\circ C$$ *Note: A change of $6.9^\circ C$ is equal to a change of $6.9\,K$.* 4. **Calculate the heat evolved (q) by the solution:** $$q = m \times c \times \Delta T$$ $$q = 100\,g \times 4.2\,J\,g^{-1}\,K^{-1} \times 6.9\,K = 2898\,J \approx 2.9 \times 10^3\,J$$ 5. **Calculate the number of moles of reactants:** The reaction is: $$NaOH(aq) + HCl(aq) \rightarrow NaCl(aq) + H_2O(l)$$ * Moles of NaOH = $\frac{M \times V(cm^3)}{1000} = \frac{1.0\,mol\,L^{-1} \times 50\,cm^3}{1000\,cm^3\,L^{-1}} = 0.05\,mol$ * Moles of HCl = $\frac{1.0\,mol\,L^{-1} \times 50\,cm^3}{1000\,cm^3\,L^{-1}} = 0.05\,mol$ Since the stoichiometry is 1:1, $0.05$ moles of NaOH react with $0.05$ moles of HCl to produce $0.05$ moles of water. 6. **Calculate the molar heat of neutralization ($\Delta H_n^\circ$):** The heat calculated ($2.9 \times 10^3\,J$) was released by the formation of $0.05$ moles of water. $$\text{Heat per mole} = \frac{\text{Total Heat}}{\text{Number of moles}} = \frac{2.9 \times 10^3\,J}{0.05\,mol} = 58000\,J\,mol^{-1} = 58.0\,kJ\,mol^{-1}$$ 7. **Determine the final enthalpy change:** Since heat is evolved (exothermic reaction), the enthalpy change is negative. The process occurs at constant pressure, so $q_p = \Delta H$. $$\Delta H_n^\circ = -58.0\,kJ\,mol^{-1}$$ ## Possible Questions/Answers **Q: What is the key difference between heat and temperature?** **A:** Heat is the *total* kinetic energy of all particles in a substance and depends on the number of particles. Temperature is the *average* kinetic energy of the particles and does not depend on the number of particles.