2.5
Enthalpy and Heat Capacity
Enthalpy (H) is a thermodynamic quantity that combines the internal energy of a system with the product of its pressure and volume. It can be mathemat…
Enthalpy, H, is a state function that combines a system's internal energy with pressure and volume.
The change in enthalpy equals the heat absorbed or released by the system at constant pressure.
Consider two cylinders, A and B, containing an ideal gas but under different conditions.
Cylinder A is sealed, so when it is heated, all the applied heat increases the system’s internal energy. Cylinder B, on the other hand, allows expansion upon heating and uses heat for both work and increasing the system's internal energy.
For cylinder A operating at constant volume, the internal energy increases with temperature. For cylinder B, maintained at constant pressure, the energy supplied equals the change in enthalpy, which also increases with temperature.
A plot of enthalpy versus temperature shows that a system’s enthalpy increases as its temperature rises at constant pressure. The slope of the tangent to this curve gives the heat capacity at constant pressure, Cp.
Likewise, a plot of internal energy versus temperature shows that internal energy increases at constant volume, and the slope of its tangent defines the heat capacity at constant volume, Cv.
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Q1: What is enthalpy and how does it relate to internal energy?
Enthalpy (H) is a state function combining a system's internal energy with the product of pressure and volume, expressed as H = U + pV. Since internal energy, pressure, and volume are state functions, enthalpy is also a state function. However, only changes in enthalpy (ΔH) can be measured, not absolute values for specific substances.
Q2: Why does enthalpy change equal heat at constant pressure?
At constant pressure, the change in enthalpy (ΔH) equals the heat (q) absorbed or released by the system. When a system loses heat to surroundings, like burning wood, ΔH is negative and the process is exothermic. When a system gains heat, like a cold pack, ΔH is positive and the process is endothermic.
Q3: How do constant volume and constant pressure conditions affect heat distribution differently?
In a sealed cylinder at constant volume, all applied heat increases internal energy. In an open cylinder at constant pressure, heat is distributed between work done during expansion and increasing internal energy. This difference explains why heat capacity varies between constant volume (Cv) and constant pressure (Cp) conditions.
Q4: What does the slope of an enthalpy-temperature plot represent?
The slope of the tangent to an enthalpy versus temperature plot at constant pressure gives the heat capacity at constant pressure (Cp). Similarly, the slope of an internal energy versus temperature plot at constant volume defines the heat capacity at constant volume (Cv). These slopes quantify how much heat is needed to raise temperature.
Q5: What is the difference between heat capacity and molar heat capacity?
Heat capacity (C) is the amount of heat required to raise a substance's temperature by one degree Celsius and depends on the amount of substance, making it an extensive property. Molar heat capacity is heat capacity divided by moles, making it an intensive property independent of substance amount.
Q6: How does temperature affect a system's enthalpy at constant pressure?
A system's enthalpy increases as its temperature rises at constant pressure. This relationship is linear and can be visualized on an enthalpy-temperature plot, where the positive slope indicates that higher temperatures correspond to higher enthalpy values. The rate of this increase is quantified by heat capacity at constant pressure.
Q7: Why can't we measure absolute enthalpy values for substances?
Absolute enthalpy values cannot be measured because enthalpy depends on internal energy, pressure, and volume—all of which have arbitrary reference points. Only changes in enthalpy (ΔH) between two states can be determined experimentally, making it a practical measure for thermodynamic calculations and applications.