Thermodynamics and Calorimetry - Key Terms

Class logistics and scope

Exam planning and review structure discussed
- Official exam number one scheduled for Wednesday, 24 September. Students should arrange accommodations with OA if needed.
- A review period will occur the day before the exam to catch up and address topics that may appear on the exam.
- Focus areas (as per the course): Focus 1 and Focus 2 from the book, covering gases and thermodynamics respectively.
Calorimetry and thermodynamics context introduced
- Calorimetry as a practical method to measure heat exchange and relate it to thermodynamic quantities like internal energy and enthalpy.
- The talk distinguishes constant-volume and constant-pressure conditions and how heat measurements relate to ΔU and ΔH.
Practical lab equipment mentioned
- DSC (Differential Scanning Calorimetry) introduced as a precise, care-controlled calorimetry method where a known amount of heat is applied and temperature change is measured.
- The instructor notes it as common lab equipment; invites students to look it up if curious about availability at Auburn.

Internal energy (U) and enthalpy (H)
- Definition:
- H = U + pV
- Differential form:
- dH = dU + p \, dV + V \, dp
Work and the first law (brief reminder)
- Work for PV processes: dw = p \, dV (for a quasi-static, simple compressible system)
- First law in differential form: dU = \,\delta q - \delta w = \delta q - p \, dV
Connection between dH and heat under mechanical conditions
- Substituting into the differential for H yields:
- dH = \delta q + V \, dp
- Mechanical equilibrium simplification (typical classroom assumption): if pressure is effectively constant during the process, then dp = 0 and thus
- dH = \delta q_p
- Consequently, at constant pressure, the heat exchanged with the surroundings equals the enthalpy change: \Delta H = q_p
Constant-volume case
- At constant volume, there is no PV-work: \Delta U = q_v

Calorimeter concept
- Calorimeter constant (C_cal): the heat capacity of the calorimeter setup.
- In practice, calorimeters translate a heat input into a measurable temperature change via: q{cal} = C{cal} \Delta T
- Molar version (per mole of substance involved): generally written as q{cal} = n \, C{cal,m} \Delta T, where $n$ is moles of substance interacted with the calorimeter.
How calorimetry relates to ΔU and ΔH
- From calorimetry, one can measure the heat associated with a process at a given condition.
- If the process occurs at constant volume: \Delta U = q_v.
- If the process occurs at constant pressure: \Delta H = q_p.
Practical note on CP (heat capacity at constant pressure)
- $C_p$ is an extensive property (scales with amount of substance).
- For small temperature changes, $C_p$ is approximately constant:
- Cp \approx \left(\frac{\partial H}{\partial T}\right)p
- If $C_p$ is constant over the temperature range of interest, the enthalpy change is
- \Delta H \approx C_p \Delta T
- More generally, for variable $C_p$,
- \Delta H = \int{T1}^{T2} Cp(T) \; dT
Summary equation tying measurement to thermodynamics
- By definition: Cp = \left(\frac{\partial H}{\partial T}\right)p \;\;\Rightarrow\;\; \Delta H \approx \int C_p \; dT
- In calorimetry, the measured heat at constant pressure equals the enthalpy change: q_p = \Delta H

Intermolecular forces and volume changes
- Solids and liquids: strong intermolecular forces; volumes change very little with temperature/pressure.
- For solids/liquids, expansion work can often be neglected due to small volume changes.
- Example scale argument (solid/liquid phase change): a calcium carbonate phase transition difference is tiny: \Delta q \approx -0.28\ \text{J mol}^{-1} (illustrative). The point