Energy and Energy Balances

• ________________– help us account for the total energy required for a process to run

• Minimizing wasted energy is crucial in ______________________________

• Energy, like mass, is _________________ _____________________. This is the ______ ____________ _________________

Components of Total Energy

• _______________– energy due to translational motion of the system as a whole to some frame of reference (usually the earth’s surface)

• _____________– energy due to the position in a gravitational or electromagnetic field

• _____________– all other energy in a system, such as __________________________ __ _______________________. Also the motion and vibration of _________________________

Energy Transfer • ________________– mass is transferred across system

boundaries during the process • ________________– no mass is transferred across its

boundaries while the process is occurring Energy can be transferred in a closed system in two ways: 1. ____ – energy that flows as a result of temperature

difference between a system and its environment. ____ __________________________. By convention in F&R _____________when it goes to the system from its surroundings

2. _____ – energy that flows for some reason other than temperature – force, torque, voltage. By convention in F&R, _______________when it is done by the system on the surroundings

Work and Heat

• ________________________________________discussing energy transfer between the system and its surroundings

• Energy has units of force x distance (eg. joules, ft-lbf)

• It also can have units defined by the amount of heat that must be transferred to raise a certain _______________________________________ _______________________________________

• Examples: calories and BTUs

First Law

• Energy (kinetic, potential, and internal) carried into a system by input streams plus the rate it enters as heat, minus the energy carried out _____________________________________ _____________________________________ _____________________________________

• Very similar to the general mass balance

• __________________________________

Kinetic Energy

• ______________

• Ek – kinetic energy

• m – mass

• u – velocity relative to surface of the earth

• Note: Ek and m may be expressed as rates when a fluid enters a system – ____________ _____________________________________

Potential Energy

• _________________ • Ep – potential energy • m – mass • g – acceleration due to gravity • z – height above a reference plane where Ep is

arbitrarily assigned a value of 0 • Ep and m may be expressed as rates – the rate at which

gravitational potential energy is transported into a system

• _____________________________________________ ________________________________________

Energy balances on closed systems

• Final system energy – initial system energy = net energy transferred to the system (in-out)

__________________________________________

• △U: final system internal energy – initial system internal

energy • △Ek: ______________________– initial system kinetic energy • △Ep: final system potential energy – initial system potential

energy • Q: heat transferred to the system by its surroundings • W: ___________________________________________

Points of interest on closed system energy balances

1. Internal energy depends mainly on chemical composition, state (S, L, or G), and temperature of materials. It is almost independent of pressure.

_____________________________________ _____________________________________ _____________________________________ ________________

_________________________________________________ __________________________

Points of interest on closed system energy balances

2. If a system is not accelerating, △Ek = 0

_________________________________________

3. If a system and its surroundings are at the same temperature, or the system is perfectly insulated, then Q=0. _________________________________

4. Work done on or by a closed system is accomplished by movement of the system boundary against a resisting force, or the passage of electric current across the boundary. Example: piston movement or shaft rotation. _______________________________ _________________________________________

Example

A gas is contained in a cylinder fitted with a movable piston. The initial gas temperature is 25°C.

The cylinder is placed in boiling water with the piston held in a fixed position. Heat in the amount of 2.00 kcal is transferred to the gas, which equilibrates at 100°C and a higher pressure. The piston is then released, and the gas does 100 J of work in moving the piston to its new equilibrium position. The final gas temperature is 100°C.

Write the energy balance for each of the two stages of the process, and in each case solve for the unknown energy term. In solving the problem, consider the gas to be the system, neglect the change in potential energy of the gas as the piston moves, and assume ideal gas behavior. Express all energies in joules.

• Stage 1:

• Stage 2:

Energy Balances: Open Systems at SS

• _____________- mass crossing system boundaries

• Work must be done to push mass in

• Work done on surroundings by mass that emerges

• ____________________________________

Flow work and Shaft work

•_______________– rate of work done by the process fluid on a moving part within the system (eg. a pump rotor) •______________– rate of work done by the fluid at the system outlet minus the rate of work done on the fluid at the system inlet

Flow Work

_______________________________ ________________________________

Specific Properties and Enthalpy

• ________________– intensive quantity obtained by dividing an extensive property by the total amount of the process material

• Example: if there are 200 cm3 of a fluid (extensive) and 200 g is its mass (extensive) the _______________is 1 cm3/g (intensive)

• If the rate ate which kinetic energy is transported by a stream in is 300 J/min and the mass flow rate is 100 kg/min, ____________________ ___________________________________

• In our text, specific properties are denoted by a ^

Specific Enthalpy

• Easily calculated using specific internal energy, total pressure, and specific volume

• Often ____________________________ __________________________________

Steady State Open-System Energy Balance

• 1st law of thermo for a open system at SS:

_______________________________ ________________________________

• Input: total rate of transport of KE, PE, IE and heat

• Output: ____________________________ _____________

SS Open-System Energy Balance

By considering all terms (potential, kinetic, internal energy, PV work, and shaft work) the first law can be written as:

This equation states that the ____________ __________________________________ _________________________ the difference between the rates at which the quantity is transferred into and out of the system

SS Open-System Energy Balances

How would the general equation for the energy balance of an open-system at steady state change in the following conditions?

1. ________________________ 2. No temperature change between system and its

surroundings 3. _________________________________ 4. All streams enter and leave at the same height

Example

Steam at 260°C and 7.00 bar absolute is expanded through a nozzle to 200°C and 4.00 bar. Negligible amounts of heat are transferred from the nozzle to its surroundings. The approach velocity of the steam is negligible. The specific enthalpy of the steam is 2974 kJ/kg at 260°C and 7.00 bar and 2860 kJ/kg at 200°C and 4.00 bar. What is the velocity in m/s of the exit steam?

Reference State and State Properties

• It is not possible to measure exact values of ___________________________________

• One can measure changes in the two by holding all other variables constant

• _____________: a temperature, pressure, and state of aggregation to which changes in specific internal energy or enthalpy can be compared

Reference State

• For example, we can measure the changes in enthalpy for CO going from a reference state of 0°C and 1 atm to two other states:

CO(g, 0°C, 1 atm) CO(g, 100°C, 1 atm)

CO(g, 0°C, 1 atm) CO(g, 500°C, 1 atm)

• Because we don’t know specific enthalpy absolutely, we can assign the reference state a ____________________________________ _______________________

Reference States

This doesn’t mean that at 500°C the absolute value is 15,060 J/mol, _________________ ___________________________________ ________________________________

Reference States

• You may or may not know the reference state used to generate this type of table

• ___________________________________ ________________________________

• That is because specific enthalpy and specific internal energy are state properties

• ______________– property that depends on the current state of the system, not the path it took to reach that state

Steam Tables

• _____________– contains as much energy as possible without boiling

• _____________ contains as little energy as possible without condensing

• _________________ ______________

Steam Tables

• Physical properties of liquid water, saturated steam, and superheated steam have been tabulated in ________________

• Steam tables can be found in Tables B.5 (Saturated Steam: Temps), B.6 (Saturated Steam: Pressure), and B.7 (Superheated steam)

• ___________________________________ ___________________________

•Properties of saturated liquid water and steam •Column 2 – pressure corresponding to temperature in Column 1 – vapor pressure of water at the temperature. One could also find the pressure and get the boiling temperature from column 1 •Columns 3,4 – specific volume of water and steam at the given temperature. ___________________________ •Columns 5,6 – specific internal energies relative to the reference state (triple point) •Columns 7-9 – specific enthalpies and the heat of vaporization. ____________ ___________________________

Saturated Steam

•Gives specific enthalpy, internal energy, and volume at any point, not just those on VLE curve •Inside the shape – liquid •Outside the shape – ___________ _________________ •The temperature below the pressure in column 1 is the boiling point •Saturated values are given in columns 2 and 3 •From superheated steam, move all the way to the left to _________ _______________________

Using the steam tables

• Determine the vapor pressure, specific internal energy, and specific enthalpy of saturated steam at 133.5°C

• Show that water at 350°C and 10 bar is superheated steam. Determine its specific volume, specific internal energy, and specific enthalpy relative to its triple point. What is its dew point?

Saturated Steam

Example

Steam at 10 bar absolute with 145°C of superheat is fed to a turbine at a rate of 2000 kg/h. The turbine operation is adiabatic, and the effluent is saturated steam at 1 bar. Calculate the work output of the turbine in kilowatts, neglecting kinetic and potential energy changes.

Liquid Water Properties

• If you need specific enthalpy for liquid water at a T and P not found in these tables, use the following procedure to estimate:

1. _____________________________________ _____________________________________

2. Assume these are independent of pressure and calculate specific enthalpy using the definition of enthalpy (___________)

3. If the pressure is not excessive (less than 10 bar), just use the value for saturated liquid given in B.5

Energy Balances

• Properly _____________________________ _______________________________

• Be sure to include all you need to know to determine enthalpies (temperature, pressure, state)

• In Chapter 7, _______________________ __________________________________ ____________

Energy Balance Procedures

1. Determine (if possible) the flow rates of all stream components ____________________

2. Determine the specific enthalpies of _____ ________________(we may have to include multiple enthalpies if there are ___________ ____________________

3. Write the appropriate form of the______ ____________________________________

Example

A 10.0 m3 tank contains steam at 275°C and 15.0 bar. The tank and its contents are cooled until the pressure drops to 1.2 bar. Some of the steam condenses in the process.

(a) What is the final temperature of the tank contents?

(b) How much steam condensed?

(c) How much heat was transferred from the tank?

A mixture containing 65.0 mole % acetone (Ac) and the balance acetic acid (AA) is separated in a continuous distillation column at 1 atm. The overhead stream from the column is a vapor that passes through a condenser. The condensed liquid is divided into two equal streams: one is taken off as the overhead product (distillate) and the other (the reflux) is returned to the column. The bottom stream from the column is a liquid that is partially vaporized in a reboiler. The liquid stream emerging from the reboiler is taken off as a bottoms product, and the vapor is returned to the column as boilup. Negligible heat is lost from the column, so that the only places in the system where external heat transfer takes place are the condenser and the reboiler.

a. Taking 100 mol of feed as a basis, calculate the net heat requirement (cal) for the process. Assume heat of mixing is negligible

b. For the same basis, calculate the required heat input to the reboiler and the required heat removal from the condenser.

Mechanical Energy Balances

• Sometimes changes in ___________________________ _____________________are more important than heat and internal energy

• In such cases, we do ______________________________ • Usually involve flow of fluids within processes • Mechanical Energy Balance General Form:

• Valid for steady state flow of an incompressible fluid • ________________________________________________

________________________________________________

Bernoulli Equation

Simplified mechanical energy balance in which friction is ______________and ____________ is performed

Example

Water flows through the system shown here at a rate of 20 L/min. Estimate the pressure required at pt 1 if friction losses are negligible.