Calculation of Enthalpy Changes: Basic Principles and Calculations in Chemical Engineering

Basic Principles and Calculations in Chemical Engineering
Dr. Nada N. Abdulrazzaq

Chemical Engineering Department – college of Engineering – University of Baghdad
Lec. No. 7
Calculation of Enthalpy Changes
1. Introduction
In this lecture we explain how you can look up and/or calculate values of the enthalpy and internal
energy to use in the energy balances. We will look at the following sources of retrieving enthalpy
data:
1. Equations to estimate the enthalpy of a phase transition
2. Heat capacity equations
3. Tables
2. Enthalpy change for Phase transition

Phase transitions occur from the solid to the liquid phase, and from the liquid to the gas phase, and
vice versa. During these transitions very large changes in the value of the enthalpy (and internal
energy) of a substance occur, changes called latent heat changes, because they occur without any
noticeable change in temperature. Because of the relatively large enthalpy change associated with a
phase transition, it is important to get accurate values of any latent heats involved when applying
energy balances. For a single phase, the enthalpy varies as a function of the temperature, as illustrated
in Figure 23.1. The enthalpy changes that take place within a single phase are usually called sensible
heat changes.
The enthalpy changes for the common specific phase transitions are termed heat of fusion (for
melting), ΔHfusion, and heat of vaporization (for vaporization), ΔHν. The word heat has been carried
by custom from very old experiments in which enthalpy changes were calculated from experimental
data that frequently involved heat transfer. Enthalpy of fusion and vaporization would be the proper
terms, but they are not widely used. Heat of condensation is the negative of the heat of vaporization
and the heat of solidification is the negative of the heat of fusion. The heat of sublimation is the
enthalpy change from solid directly to vapor.
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The overall specific enthalpy change of a pure substance, as illustrated in Figure 23.1, can be
formulated by summing the sensible and latent heats (enthalpies) from the initial state to the final
state.
Figure 23.1. The overall enthalpy change includes the sensible heats (the enthalpy changes
within a phase) plus the latent heats (the enthalpy changes of the phase transitions).
𝑇2
Note that Equation 𝛥𝐻 = ∫𝑇1 𝐶𝑝 𝑑𝑇 is to calculate the enthalpy change for single phase ant it is
not valid if a phase change occurs. The enthalpy associated with a phase change (Equation 23.1) must
be included to get the overall ΔH (or ΔĤ).
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There are many equations available to calculate the enthalpy of vaporization ΔHν, the most famous
one is the Clausuis Calpeyron Equation:
𝑝2 𝛥𝐻𝑣 1 1
𝑙𝑛 =− ( − )
𝑝1 𝑅 𝑇2 𝑇1
𝑝1 is the vapor pressure at temperature 𝑇1
𝑝2 is the vapor pressure at temperature 𝑇2
𝛥𝐻𝑣 is the enthalpy of vaporization
R is gas constant
3. Enthalpy change from heat capacity equations

As we mentioned before that the enthalpy change for single phase (not for phase transitions) can be
calculated using the heat capacity (𝐶𝑝 ):
𝑇2
𝛥𝐻 = ∫ 𝐶𝑝 𝑑𝑇
𝑇1
If 𝐶𝑝 constant, 𝛥𝐻 = 𝐶𝑝 𝛥𝑇 where 𝛥𝑇 = 𝑇2 − 𝑇1
If 𝐶𝑝 is given as a function of temperature, it will take the following empirical equation form which
is usually given for a specified range of temperature:
𝐶𝑝 = 𝑎 + 𝑏𝑇 + 𝑐𝑇 2
Where 𝑇 may be expressed in C, K, F,R
So 𝛥𝐻 will be:
If we have gas mixture of N components then we should calculate the 𝐶𝑝 𝑛𝑒𝑡 for this mixture:
61
𝑁
𝐶𝑝 𝑛𝑒𝑡 = ∑ 𝐶𝑝𝑖 𝑦𝑖
𝑖=1
𝐶𝑝 𝑛𝑒𝑡 is the total specific heat for the mixture
𝐶𝑝𝑖 is the specific heat of each component in the gas mixture
𝑦𝑖 is the mole fraction of each component in the gas mixture
N number of components
Example 1:
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Example 2:
Calculate the enthalpy change for the transition of 1 Kg of water from -30C to 130C using the
data at Figure 23.5 plus values of 𝐶𝑝 of:
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So the total 𝛥𝐻 will be:
4. Tables and charts to retrieve enthalpy values

Tables like Steam Tables can cover the values of physical properties well beyond the range valid for
a single equation. Because the most commonly measured properties are temperature and pressure,
tables of enthalpies (and internal energies) for pure compounds usually are organized in columns and
rows, with T and p being the independent variables.
If the intervals between table entries are close enough, linear interpolation between entries is
reasonably accurate. For example, look at the following extract from the steam tables for saturated
steam in SI units. If you want to calculate the enthalpy of saturated steam at 307 K by linear
interpolation you would carry out the following computation:
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You can find the enthalpy of other components (other than water) in appendix D6 at the end of the
book.
Problems
1. Calculate the enthalpy change for 1 kg of N2 gas that is heated at a constant pressure of 100 kPa from
18C to 1100C.
̂?
2. Steam is cooled from 640F and and 92 psia to 480F and 52 psia. What is 𝛥𝐻
3. Two gram moles of nitrogen are heated from 50C to 250C in a cylinder what is the enthalpy change
for the process? The heat capacity equation is:
𝐶𝑝 = 27.32 + 0.6226 × 10−2 𝑇 − 0.0950 × 10−5 𝑇 2
4. The normal boiling point of methanol is 64.7C. calculate its boiling point at an elevation of 4000 m
above sea level where the pressure is 478 mmHg. The heat of vaorization of methanol is 35.3 kJ/
mol?
5. Use steam tables to calculate the enthalpy change of 2 kg mol of steam heated from 400 K and 100
kPa to 900 K and 100 kPa. Reapeat using the heat capacity of steam compare your results.
6. Calculate the enthalpy change that occur in raising the temperature of 1 kg mol of the gas mixture
(CH4 80%, C2H620%) from 50 to 550C
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Basic Principles and Calculations in Chemical Engineering

Dr. Nada N. Abdulrazzaq

Calculation of Enthalpy Changes

2. Enthalpy change for Phase transition

3. Enthalpy change from heat capacity equations

Where 𝑇 may be expressed in C, K, F,R

4. Tables and charts to retrieve enthalpy values

𝐶𝑝 = 27.32 + 0.6226 × 10−2 𝑇 − 0.0950 × 10−5 𝑇 2

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