Energy Balance B.Sc. II Semester Industrial Chemistry

ICB-251

Wasi ur Rahman

Introduction

• Process industries have always recognized that wasting energy

leads to reduced profits, but throughout most of this century the

cost of energy was often an insignificant part of the overall process

cost, and gross operational inefficiencies were tolerated. In the

1970s, a sharp increase in the price of natural gas and petroleum

raised the cost of energy several fold and intensified the need to

eliminate unnecessary energy consumption. If a plant uses more

energy than its competitors, its product could be priced out of the

marketplace.

Total Energy

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 energy.

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 sys- tem, 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.

Heat and Work

Suppose a process system is closed, meaning that no mass is transferred across its

boundaries while the process is taking place. Energy may be transferred between

such a system and its surroundings in two ways:

1.As heat, or energy that flows as a result of temperature difference between a

system and its surroundings. The direction of flow is always from a higher

temperature to a lower one. Heat is defined as positive when it is transferred to the

system from the surroundings.

2.As work, or energy that flows in response to any driving force other than a

temperature difference, such as a force, a torque, or a voltage. For example, if a gas

in a cylinder expands and moves a piston against a restraining force, the gas does

work on the piston (energy is transferred as work from the gas to its

surroundings, which include the piston).

• Ek = 1 /2mu2

Ek = 1/2 mu2

KINETIC AND POTENTIAL ENERGY

The kinetic energy, Ek(J), of an object of mass m(kg) moving with velocity

u(m/s) relative to the surface of the earth is

If a fluid enters a system with a mass flow rate m (kg/s) and uniform velocity u(m/s),

Ek(J/s) may be thought of as the rate at which kinetic energy is transported into the

system by the fluid.

Solved problem

Potential Energy

Solved Example

Problem. 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 ground level. Calculate the attendant rate of

increase of potential energy.

ENERGY BALANCES ON CLOSED SYSTEMS

A system is termed open or closed according to whether or not mass crosses the system boundary

during the period of time covered by the energy balance. A batch process system is, by definition,

closed, and semi batch and continuous systems are open. An integral energy balance may be

derived for a closed system between two instants of time. Since energy can neither be created nor

destroyed, the generation and consumption terms of the general balance drop out, leaving

accumulation = input — output (7.3-1)

In deriving the integral mass balance for a closed system in Section 4.2c we eliminated the

input and output terms, since by definition no mass crosses the boundaries of a closed system. It

is possible, however, for energy to be transferred across the boundaries as heat or work, so that

the right side of Equation 7.3-1 may not be eliminated automatically. As with mass balances,

however, the accumulation term equals the final value of the balanced quantity (in this case,

the system energy) minus the initial value of this quantity. Equation 7.3-1 may therefore be

written

Solved example

Problem. 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 equation for each of the two stages of this

process, and in each case solve for the unknown energy term in the

equation. In solving this problem, consider the gas in the cylinder to be the

system, neglect the change in potential energy of the gas as the piston moves

vertically, and assume the gas behaves ideally. Express all energies in joules.

Flow Work and Shaft Work

The net rate of work done by an open system on its

surroundings may be written as . . . W = Ws + Wfl

Where

• Ws = shaft work, or rate of work done by the process fluid

on a moving part within the system (e.g., a pump rotor)

Wfl = flow work, or rate of work done by the fluid at the system

outlet minus the rate of work done on the fluid at the system

.inlet

Open system steady State

• Above equation states that the net rate at which energy is

transferred to a system as heat and/or shaft work (Q — Ws) equals

the difference between the rates at which the quantity (enthalpy. +

kinetic energy+ potential energy) is transported into and out of the

system (H + Ek+ Ep). We will use this equation as the

starting point for most energy balance calculations on open

systems at steady state.

Solved example

• Problem. Five hundred kilograms per hour of steam drives a

turbine. The steam enters the turbine at 44 atmand 450 C at a

linear velocity of 60 m/s and leaves at a point 5 m below the

turbine inlet at atmospheric pressure and a velocity of 360 m/s.

The turbine delivers shaft work at a rate of 70 kW, and the heat

loss from the turbine is estimated to be 10 kcal/h. Calculate the

specific enthalpy change associated with the process

Solution

• Course is completed, for any clarification, You may

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