### Energy/Mass Balance - 5 of 80 Problems

Energy/Mass Balance accounts for approximately 5 questions on the HVAC & Refrigeration Mechanical PE exam. This section focuses on the energy and mass balance equations that govern various HVAC and Refrigeration processes. These processes include evaporation, condensation and mixing. The important concept to understand is that in each process, energy and mass of the fluid is conserved, even if the fluid is changing from gas to liquid or liquid to gas.

### Conservation of Energy

Conservation of energy is a law in nature and states that energy cannot be created or destroyed. Therefore, when transfers of states or changes in phases occur in a system, an energy balance equation can be created to solve for the unknown properties in a system or cycle.

Turbines, pumps and compressors change the amount of energy of the incoming fluid by changing the pressure of the fluid. Pumps and compressors increase the pressure of the fluid, while turbines reduce the pressure of the fluid. In a pump and compressor, energy is transferred from a power source to the fluid. In a turbine, energy is transferred from a fluid to provide a power source. In both cases, this power source is called Work. Essentially work is transferred to or from these pieces of equipment.

Boilers, condensers and evaporators are pieces of equipment where a phase change in a fluid occurs. In boilers and evaporators, liquid is changed to gas and in condensers, gas is changed to liquid. In boilers and evaporators, energy is added into the system by the boiler or evaporator in order to heat the liquid to gas. In condensers, heat is removed from the system by the condenser in order to change the gas to a liquid. The energy balance equations governing these pieces of equipment take into account the phase change of the fluids.

Heat exchangers are used to transfer heat from one fluid the other. Heat exchangers can be used to transfer heat from one hot liquid to a cold liquid, a hot air stream to a cold air stream, from air to liquid or from liquid to air. Since there is no phase change, the energy balance equation is only based on the mass flow rate of both fluids, the temperatures of these fluids and the heat capacity of both fluids.

In feedwater heaters or in tanks, two fluids may be mixed together. The energy balance on these types of systems involves calculating the total energy of the fluids entering the system, which will equal the energy of the mixed fluid. A few equations shown below highlight this relationship. This mixing energy balance can be applied to both air and liquid. Similarly to boilers, condensers and evaporators, if a phase change occurs, then the energy change due to the phase change must be taken into account.

### Conservation of Mass

Conservation of mass is a law in nature and states that mass cannot be created or destroyed. Therefore, when transfers of states or changes in phases occur in a system, a mass balance equation can be created to solve for the unknown properties in a system or cycle.

Essentially, the equations are derived from the law that:

Similarly, the flow of mass entering the system will be equal to the flow of mass leaving the system, like in a condenser or a boiler.

The figure above shows one pound of steam entering a condenser and leaving as one pound of water.

The figure above shows one pound of water entering a boiler and leaving as one pound of steam. See technical study guide for continuation.

### Evaporation

Evaporation is a change in state from liquid to a gas. The phase change occurs when there is enough heat or when the pressure is low enough for the liquid to convert to gas.

During the evaporative process the mass of the water will equal to the mass of the evaporated gas. See technical study guide for continuation.

### Condensation

Condensation is the opposite of evaporation. During condensation, molecules in the gaseous state lose sufficient energy to turn into a liquid or the pressure is high enough for the gas to be converted to a liquid.

During the condensation process the mass of the gas will equal the mass of the condensed liquid.

The equations for condensation are the same as evaporation but in reverse, where the mass flow rate of the entering vapor is equal to the mass flow rate of the leaving liquid.See technical study guide for continuation.

### Dehumidification and Humidification

The process of dehumidification and humidification is the process of either adding or removing moisture from air.

Dehumidification is the process of removing moisture from air and can be referred to as latent cooling. Humidification is the process of adding moisture to air and can be referred to as latent heating. These terms are explained more in the Psychrometrics section of the Support Knowledge topic. But in this Mass Balance section, the governing equations follow the conservation of mass of the water. The rate of change of the moisture in air is equal to the mass flow rate of air multiplied by the change in moisture content in the air. The change in moisture content of the air is given as the specific humidity of the air at the entering and leaving conditions of the humidifier or dehumidifier. This change in mass flow rate of moisture in the air must equal to the mass flow rate of water added by the humidifier or removed by the dehumidifier.

These figures show a humidifier and a dehumidifier. The mass flow rate of water into and out of the equipment must equal the moisture gain or loss in/from the air.

### Mixing

A common skill is determining the output conditions of the mixture of two fluid streams, which could be liquid-liquid, liquid-gas or gas-gas. Since mass balance does not depend on the phase of the fluid, then the mass balance equations will still apply.

The important concept to first understand is that the output conditions of the mixed fluid stream will be most similar to the fluid stream that has the most mass flow rate.

The second concept is that when two liquids or two gases mix together, then the resulting mixed gas or liquid mass flow rate is equal to the sum of both entering liquids/gases.

If there is a gas and a liquid entering a device, then it is more difficult to determine the mixed gas and liquid flow rate leaving the device, because some of the gas may condense or some of the liquid may evaporate. See technical study guide for continuation.