The General Energy Balance

p (kPa) Satn. temp., hCQ Volume (cm /g) Enthalpy (J/g)  

Fire walkers with bare feet walk across beds of glowing coals without apparent harm. The rite is found in many parts of the world today and was practiced in classical Greece and ancient India and China, according to the Encyclopaedia Britannica. 

The temperature of glowing coals is about 1000°C. What are some of the possible reasons that fire walkers are not seriously burned  

The heat weakens the tank shell around the ullage space. Thermally induced stresses are created in the tank shell near the vapor/Iiquid interface, and the heat-weakened tank plus the high internal pressure combine to cause a sudden, violent tank rupture. Fragments of the tank are propelled away from the tank at great force. Most of the remaining superheated liquid vaporizes rapidly due to the, pressure release. The rest is mechanically atomized to small drops due to the force of the explosion. A fireball is created by the burning vapor and liquid. 

What steps would you recommend to prevent a BLEVE in the case of fire near a storage tank Hint Two possible routes are (1) prevent the fire from heating the tank and (2) prevent the buildup of presure in the tank.] 

---

In considering the flow in a pipe, the differential form of the general energy balance equation 2.54 are used, and the friction term 8F will be written in terms of the energy dissipated per unit mass of fluid for flow through a length d/ of pipe. In the first instance, isothermal flow of an ideal gas is considered and the flowrate is expressed as a function of upstream and downstream pressures. Non-isothermal and adiabatic flow are discussed later. 

Referring to Fig. 4.7, the general energy balance for segment n with S components and R reactions is... 

All the examples of energy balances considered previously have been for steady-state processes where the rate of energy generation or consumption did not vary with time and the accumulation term in the general energy balance equation was taken as zero. 

The general energy balance for an element of volume AV over a time At can be written as ... 

Additional cases applied to the general energy balance are ... 

Assuming a steady state process (AE = 0), no kinetic (KE) or potential energy (PE) changes and mechanical work done (W) by the system on the surroundings are zero, that is KE, PE, and W = 0, the general energy balance... 

Consider the elemental volume S81 at length 1 of the plug flow. Applying the general energy balance in differential form gives... 

In most equilibrium stage processes, the general energy balance can be simplified by neglecting potential energy and kinetic energy. If, in addition, the process is workless and adiabatic, a simple enthalpy balance applies ... 

The general energy balance for steady-state flow processes is given by Eq. (7.8) ... 

The kinetic and potential energy effects can be neglected ( = 0). There is no exchange of heat with the surroundings (Q = 0). The general energy balance reduces to AH = W Note that the value of W is positive (work done on the system). ... 

Show that the general energy balance, Equation (9.3.9), can simplify to an appropriate form for either adiabatic or isothermal reactor operation. 

Suppose sys(f) is the total energy (internal + kinetic + potential) of a system, and ihm and /hout are the mass flow rates of the system input and output streams. (If the system is closed, these quantities each equal zero.) Proceeding as in the development of the transient mass balance equation, we apply the general energy balance equation (11.3-1) to the system in a small time interval from t to t + 1st, during which time the properties of the input and output streams remain approximately constant. The terms of the equation are as follows (see Section 7,4) ... 

Finally, we may substitute the expressions of Equations 11.3-3 through 11.3-11 into the general energy balance (Equation 11.3-2) to obtain for an open system... 

The present photodissociation results can be used to help interpret such a picture. For illustration, we choose a definite model. The general energy balance for the reactions is... 

In this section we apply the general energy balance [Equation (8-22)] to the CSTR and to the tubular reactor operated at steady state. We then present example problems showing how the mole and energy balances are combined to size reactors operating adiabatically. 

Flow processes for wliich the accumulationtermof Eq. (2.28), d mU v/dt, is zero are said to occur at steady state. As discussed with respect to tire mass balance, tliis means tliat tire mass of the system within the control volume is constant it also means that no changes occur with time in tire properties of tire fluid witliin the control volume nor at its entrances and exits. No expansion of the control volume is possible under these circumstances. The only work of the process is sliaft work, and the general energy balance, Eq. (2.28), becomes ... 

Before formulating the general energy balance, we shall discuss in some detail the calculation of enthalpy changes and provide some typical examples of such calculations. Our discussion will be initiated with consideration of the heat capacity Cp. The two heat capacities have been defined as... 

Write down the general energy balance in words [Eq. (4.22)]. 

TABLE 4.8 Summary of the Symbols to be Used in the General Energy Balance... 

In most problems you do not have to use all the terms of the general energy balance equation because certain terms may be zero or may be so small that they can be neglected in comparison with the other terms. Several special cases can be deduced from the general energy balance of considerable industrial importance by introducing certain simplifying assumptions ... 

---