In the Are You Wondering 7-1 box, the temperature variation of enthalpy is discussed, and the equation was introduced to show how enthalpy changes with temperature for a constant-pressure process. Strictly speaking, the heat capacity of a substance at constant pressure is the slope of the line representing the variation of enthalpy (H) with temperature, that is

where C_p is the heat capacity of the substance in question. Heat capacity is an extensive quantity and heat capacities are usually quoted as molar heat capacities C_p, m, the heat capacity of one mole of substance, which is an intensive property. The heat capacity at constant pressure is used to estimate the change in enthalpy due to a change in temperature. For infinitesimal changes in temperature,

To evaluate the change in enthalpy for a particular temperature change, from T₁ to T₂, we write

If we assume that C_p is independent of temperature, then we recover equation (7.5)

On the other hand, we often find that the heat capacity is a function of temperature; a convenient empirical expression is

What is the change in molar enthalpy of N₂ when it is heated from 25.0 °C to 100.0 °C? The molar heat capacity of nitrogen is given by

Eq. 7.5

Transcribed Image Text:

Cp dH dT (at constant pressure)