## Solution

The first law of thermodynamics states that energy is conserved. For a flow system, neglecting kinetic and potential effects, the energy transferred, Q, to or from the flowing medium is given by the enthalpy change, AH, of the medium. The enthalpy of an ideal gas is solely a function of temperature; enthalpies of liquids and most real gases are almost always assumed to depend on temperature alone. Changes in enthalpy resulting from a temperature change for a single phase material may be calculated from the equation

where AH = enthalpy change m = mass of flowing medium cp = average heat capacity per unit mass of flowing medium across the temperature range of AT AH = enthalpy change per unit time m = mass flowrate of flowing medium

Note: The symbol A means "change in."

CLE.2 POTENTIAL ENERGY CALCULATION

Solve the conservation law for energy for the gas outlet temperature T2:

where Q is the rate of energy transfer.

The gas outlet temperature is therefore

T2 = [-18.7 x 106/{(72,000)(0.26)}] + 1200 = 200° F

The above equation is based on adiabatic conditions, i.e., the entire heat load is transferred from the flowing gas. The unit is assumed to be perfectly insulated so that no heat is transferred to the surroundings. However, this is not the case in a real-world application.

As with mass balances (see Chapter 2), an enthalpy balance may be performed within any properly defined boundary, whether real or imaginary. For example, an enthalpy balance can be applied across the entire unit or process. The enthalpy of the feed stream(s) is equated with the enthalpy of the product stream(s) plus the heat loss from the process. All the enthalpy terms must be based on the same reference temperature.

Finally, the enthalpy has two key properties that should be kept in mind:

1. Enthalpy is a point function, i.e., the enthalpy change from one state (say 200° F, 1 atm) to another state (say 400° F, 1 atm) is a function only of the two states and not the path of the process associated with the change.

2. Absolute values of enthalpy are not important. The enthalpy of water at 60° F, 1 atm, as recorded in some steam tables is 0 Btu/lbmol. This choice of zero is arbitrary however. Another table may indicate a different value. Both are correct! Note that changing the temperature of water from 60 to 100°F results in the same change in enthalpy using either table.

Enthalpy changes may be obtained with units (English) of Btu, Btu/lb, Btu/lbmol, Btu/scf, or Btu/time depending on the available data and calculation required.

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