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Enthalpy calculation with Cp

Enthalpy calculation with Cp
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Welcome to thermodynamics in energy engineering week 2. The first topic is enthalpy calculation. We can calculate enthalpy change with the help of heat capacity Cp. Keep in mind that including enthalpy, energy is not an absolute term. There is no absolute zero of energy. We can only calculate the difference between the two states of them. Let’s calculate the enthalpy change when the temperature changes from T1 to T2. Differential enthalpy changes at constant pressure dHp is CpdT. Integration on both side will give us the enthalpy changes. The temperature dependence of Cp is generally written like this. So the integration of this temperature function over the temperature of interest will be the enthalpy change.
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There is no absolute energy values, however, for convenience in tabulation, people defined the reference state for a material and assign zero enthalpy for the reference states. The reference condition is in their equilibrium state at 298K, 1 atm. The equilibrium state means the most stable phase under the given conditions. 298 K, the room temperature and 1 atm condition is called the standard state. The element in the most stable phase under the standard states is the reference state, thus have zero enthalpy, H298K nought is zero. Here the superscript nought means standard state. Look at the examples. In the standard condition at room temperature and 1 atm, the most stable form of carbon is graphite. So the enthalpy for graphite is zero.
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But the diamond is not in the equilibrium state, so the enthalpy is not zero under standard conditions. O2 gas molecule is in their most stable state, and solid iron is also the most stable phase under the standard condition, thus have zero enthalpy. The elements in their reference condition have zero enthalpies, then the compounds must have some other values of enthalpy at the reference condition. So for the compounds, enthalpy of formation is assigned for the reference condition. Enthalpy of formation is the heat of the formation reaction from their constituent elements in reference state. Let’s take iron oxide as an example. The formation reaction from their constituent elements is like this.
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So heat of this reaction under the reference condition is the enthalpy of formation of FeO.

We can calculate the energy difference between two states of different temperature if we know the heat capacities.

When the pressure is constant, integration of ({ C }_{ p }) with respect to temperature gives the energy changes upon temperature change within a single phase. This energy change under constant pressure is called sensible heat. Since we can only calculate the energy difference between two states, the concept of a reference state where the zero enthalpy is assigned might be particularly useful. Then the enthalpy of a material at a certain state is not an absolute term but the enthalpy difference from the reference state. For compounds, heat of formation is assigned for the convenience in tabulation.

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Thermodynamics in Energy Engineering

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