Energy Flows and Balances

Units of Measure

BTU – amount of energy required to heat one pound of water, one degree Fahrenheit

Calorie – amount of energy required to heat 1 ml water 1 degree Celsius

Energy Balances and Conversion

The form of the available energy is often not the form that is the most useful so it is common to have to convert one form of energy to another.

Water in lake – turbine – electricity – light and heat

Bio-mass – combustion – steam - generator - electricity

Wind – windmill – generator - electricity

Conversion always less than 100% efficient

Since energy “flows” can use the same concepts as materials balance to analyze

Rate ofEnergy

accumulated

Rate of Energy

In

Rate ofEnergy

Out

Rate of Energy

Generated= - +

At Steady-State

0

Rate ofEnergy

In

Rate ofEnergy

Out

Rate of EnergyWasted

= -

Efficiency:

Useful energy Out

Energy InX 100

Bomb Calorimeter

Calorimeter Example

A calorimeter holds 4 liters of water. When a 10 gram sample of a waste-derived fuel is combusted the result is a 12.5o C rise in temperature. What is the energy value of the fuel?

Energy In = Energy Out

(The idea behind a calorimeter is that no energy is wasted. It is all captured in the device.)

Energy Out = 12.5o C x 4 L x 103 ml/L x 1 g/ml

= 50 x 103(0C). G, or calories

= 50 x 103 calories x 4.18 (J/cal) = 209 x 103 J

Energy In = 209 x 103 J

Energy Value of the Fuel = (209 x 103 J/g)/ (10 g) = 20,900 J/g

Heat Energy

HeatEnergy

Mass ofMaterial

Absolute TemperatureOf the Material

= X

This is only true when the heat capacity of the material is independent of temperature. In particular when a phase change occurs this is not true. (Water to Steam)

Energy Balance at Steady-State with two inflows

0 = Heat Energy In - Heat Energy Out + 0

0 = [T1Q1 + T2Q2] - T3Q3

T3 = [T1Q1 + T2Q2] / Q3

Also: Q3 = Q1 + Q2

Example

A coal-fired power plant discharges 3 m3/sec of cooling water at 80o C into a river that has a flow of 15 m3/sec and a temperature of 20o C. What will the temperature of the river be immediately downstream of the discharge?

T3 = [T1Q1 + T2Q2] / Q3

= [(80 + 273)(3) + (20 +273)(15)] / (3 + 15)

= 303oK = 30o C

Energy Sources and Availability

Non-Renewable Sources

Nuclear PowerCoal, Peat, and Similar ProductsOilNatural Gas

Renewable Sources

Hydropower from RiversHydropower from TidesWood and Other Bio-massSolar PowerRefuse and other WastesWind

What responsibility do we have to future generations?

Energy Equivalence

Arithmetic Energy Equivalence – based on energy amounts only

Conversion Energy Equivalence – takes into account the energy loss in conversion

For ExampleIf gasoline has an energy value of 20,000 BTU/lb and refuse-derived fuel has an energy value of 5,000 BTU/lb, the arithmetic energy equivalence is:

20,000/5,000 = 4 lb refuse / 1 lb gasoline

It has been estimated that 50% of the energy in refuse derived fuel is required for processing, therefore, the actual net energy in the refuse is 2,500 BTU/lb. So:

Conversion energy equivalence = 20,000 / 2,500 = 8 lb refuse / 1 lb gasoline

Electric Power Production

Present power plans are less than 40% efficient

Simplified:

Heat Engine

Energy Balance

Rate ofEnergy

accumulated

Rate of Energy

In

Rate ofUseful

Energy Out

Rate of Wasted

Energy Out= - -

0, S.S.

0 = Qo - QU - QW

Efficiency (%) = QU/Qo

The most efficient engine possible is called a Carnot Engine. Its efficiency is calculated as:

EC(%) = (T1 – To)/T1 x 100

Where: T1 = absolute temperature of the boilerT2 = absolute temperature of the cooling water

Since this is the best possible:

(QU/Qo) < (T1 – To)/T1

Typical conditions for a power plant are: T1 = 600 + 273 = 873, and T0 = 20 + 273 = 293

EC = (873 – 293) / 873 = 66%

Because real power plants have many other types of energy losses (heat in stack gases, evaporation, friction) their actual efficiency is about 40%. This figure is confirmed by operational data.

Where does all of this energy go?

All of it is dissipated in some way into the environment

60% of the energy content of the fuel that comes into the plant is released to the environment as heat

15% stack gases, 45% cooling water

Thermal pollution

Cooling this water before discharge is a significant problem

Cooling towers such as these can add up to 250% to the cost of a nuclear power plant

Why is it better to allow this heat to be discharged to the atmosphere rather than to a water body?

What else could you do with this heat?