Fundamentals of Energy Balances Chapter 3 Fundamentals of Energy Balances

Energy out = Energy in + generation – consumption – accumulation CONSERVATION OF ENERGY A general equation can be written for the conservation of energy: Energy out = Energy in + generation – consumption – accumulation This is a statement of the first law of thermodynamics. An energy balance can be written for any process step. Chemical reaction will evolve energy (exothermic) or consume energy (endothermic). For steady-state processes the accumulation of both mass and energy will be zero. Energy can exist in many forms and this, to some extent, makes an energy balance more complex than a material balance.

Energy and Energy Balances Forms of Energy: The First Law of Thermodynamics The total energy of a system has three components: 1. Kinetic Energy: Energy due to the translational motion of the system as a whole relative to some frame of reference (usually the earth’s surface) or to rotation of the system about some axis. In this text, we will deal only with translational kinetic energy. …………………………………………... 2. Potential Energy: Energy due to the position of the system in a potential field (such as a gravitational or electromagnetic field). In this text, we will deal only with gravitational potential field. 3. Internal Energy: All energy possessed by a system other than kinetic and potential energy, such as energy due to the motion of molecules relative to the center of mass of the system, to the rotational and vibrational motion and the electromagnetic interactions of the molecules, and to the motion and interactions of the atomic and subatomic constituents of the molecules. ………………………

FORMS OF ENERGY 1. Potential energy Where: Energy due to position: Potential energy = gz Where: z = height above some arbitrary datum, m, g = gravitational acceleration (9.81 m/s2).

Example Crude oil is pumped at a rate of 15.0 kg/s from a point 220 meters below the earth’s surface to a point 20 meters above the ground level. Calculate the attendant rate of increase of potential energy. Solution 15.0 kg 9.81 m [20-(-220)] m 1 N = s s2 1 kg.m/s2 = 35,300 N m/s = 35,300 J/s A pump would have to deliver at least this much power to raise the oil at the given rate.

Example: Potential Energy Water is pumped from one reservoir to another 300 ft away. The water level in the second reservoir is 40 ft above the water level of the first reservoir. What is the increase in specific potential energy of the water in Btu/lbm?

FORMS OF ENERGY 2. Kinetic energy Energy due to motion: where u = velocity, m/s.

Example: Water flows into a process unit through a 2-cm ID pipe at a rate of 2.00 m3/h. Calculate Ėk for this stream in joules/second. Solution 2.00 m3 1002 cm2 1 h h (1)2 cm2 m2 3600 s 2.00 m3 1000 kg 1 h h m3 3600 s 0.556 kg/s (1.77)2 m2 1 N 2 s2 1 kg.m/s2

FORMS OF ENERGY 3. Internal energy (U): The energy associated with molecular motion. The temperature T of a material is a measure of its internal energy U: U = f(T) Energy of molecule, atom, and subatom. Internal energy per unit mass (u) can be calculated from measurable variables such as pressure, volume, temperature, and composition.

Changes in the internal energy can be computed by the following equation:

FORMS OF ENERGY HEAT (Q) Heat, Q, when used in the general energy balance, as a single term, is the net amount of heat transferred to or from the system over a fixed time interval. A process may involve more than one specified form of heat transfer, of course, the sum of which is Q. The rate of transfer will be designated by an overlay dot on Q thus: , with the units of heat transfer per unit time, and the net heat transfer per unit mass would be designated by an overlay caret thus: .

HEAT (Q) Here are some misconceptions about heat that you should avoid: • Heat is a substance. • Heat is proportional to temperature. • A cold body contains no heat. • Heating always results in an increase in temperature. • Heat only travels upward. Heat transfer is usually classified in three categories: conduction, convection, and radiation. To evaluate heat transfer quantitatively, you can apply various empirical formulas to estimate the heat transfer rate. One example of such a formula is the rate of heat transfer by convection that can be calculated from Q = U⃰A(T2 – T1)

Example: Energy Conservation Energy conservation is important for houses, commercial buildings, and so on. To what fraction is the heat transfer rate reduced by replacing a glass window 3 ft wide and 5 ft high with a smaller window 2 ft wide by 3 ft high? As a typical case, assume the outside temperature in the winter is 25°F and the inside temperature is 75°F. For this example assume U* = 5.5 Btu/(hr)(ft2)(°F). If the cost of energy is $9.50/106 Btu, how many dollars per 30-day month are saved by changing the window size if the given temperatures are constant? Solution You could calculate for each case using the below equation, but it is quicker to take a ratio: itself is negative but the savings will be positive.

Example Steam is cooled from 640 ºF and 92 psia to 480 ºF and 52 psia. What is ΔH in Btu/lb?