September 28, 2013 Diego Villarreal SHP – Columbia University Thermodynamics & Energy Conversions

2 What is energy anyway? Energy? “Capacity to do work” Different types of energy: ○ Mechanical Kinetic – Associated with object or fluid motion (KE = ½ mv 2 ) Potential – Associated with object’s position (PE=mgh) ○ Chemical energy – Energy stored in chemical bonds and released upon transformation/reaction (coal, oil, methanol) ○ Nuclear – Energy found within the atomic nucleus. Can be released by ‘breaking’ (fission) the atoms. ○ Thermal Energy – Think of it as microscopic PE & KE of an object that results in its temperature (cup of hot coffee). ○ Radiant – Energy of electromagnetic waves. ○ Electrical –

3 Wasted energy About 3/5 of the fuel energy input is “wasted”. Because our energy system is highly dependent on fossil fuels this leads to extra CO 2 and pollution. So, why is this? Is there a natural limit to how efficient we can be at our energy conversion? Need to turn to thermodynamics to answer this question.

4 Energy, Heat and work Main principles: ○ Heat spontaneously flows from Hot  Cold (Always, no exception). More formal treatment of this in a bit. ○ Energy Conservation - Energy can be transformed from one form to another, but cannot be created or destroyed. Thermodynamics – The study of the interchangeability of heat and work. ○ Think of thermodynamics as the “economics of science”. It will tell us how much we will have to “pay” for particular transformations and whether or not they are feasible. ○ Basic “bookkeeping”

5 Heat Heat (Q) is the energy transferred between a system and its surroundings (other than by work). Usually a result of a temperature difference between two objects. Heat is NOT a fluid and is never contained within an object; an object contains thermal energy. Think of ΔT as an “index” of your ability to move heat. Remember this!

6 First law of thermo First law of thermo? ○ The first law of thermodynamics states that during any cycle that a system undergoes, the cyclic integral of the heat is equal to the cyclic integral of the work. Hence, it requires that energy be conserved during a process. However, the first law places no restrictions on direction of flow. That is, work done on a system plus the heat added to it is equal to the total change in energy of the system. ΔE = W on + Q to Work done on a system is the negative of work done by the fluid (W on =- W by ) so: Q to = ΔE + W by Temperature does not tell us the amount of energy contained in a substance. However a change in temperature tells us something about the heat added (removed) Q = mcΔT

7 Second law Second law? ○ The only processes that can occur are ones that result in an increase in the entropy of the systems (e.g. direction matters!)

8 Heat Engines We know from experience that work can easily be converted to other forms of energy, but converting other forms of energy to work in not that easy. Converting heat to work requires the use of some special devices. These devices are called heat engines. 1.HE receive heat from a high-temp source 2.Convert part of this heat to work (usually by rotating shaft) 3.Reject the remaining waste heat to a low temperature reservoir. 4.Operate in a cycle

9 PV diagrams Useful tool to study heat engines. Points a  b are at constant T. Called “isotherms”. So moving from a  represents “Isothermal Expansion ”

10 Adiabatic compression Looking at the PV diagram, what is a necessary condition to perform isothermal compression/expansion? ○ Heat must be supplied or removed! So what happens if I insulate the compression chamber or do fast compression? ○ ΔQ = 0! ○ Thermal energy and T must change. ○ “Adiabatic” compression/expansion

11 Carnot Engine Let’s do a device to exchange Q and W using isotherms and adiabats. Assumptions: ○ Piston-Cylinder device ○ Perfectly insulated but insulation is such that it can be removed instantaneously to put system in contact with heat reservoir. ○ No friction, no turbulence ○ No mechanical inefficiency losses

12 Carnot Cycle Step 1-2: Isothermal Expansion Step 2-3: Adiabatic Expansion Step 3-4: Isothermal Compression Step 4-1: Adiabatic Compression

13 Carnot Efficiency W net will be area enclosed by engine cycle. Important question: what fraction of the heat supplied is converted to mechanical work? ○ Called the efficiency! ○ Efficiency = W out /Q in ○η = (Q in -Q out )/Q in For carnot engines:

14 Steam cycle The core of a steam power consists of four components: ○ a boiler, turbine, condenser, and a pump. First, fuel is burned in a furnace/boiler where the released heat is transferred to pressurized water contained within steel tubes. Then, the high-pressure, high- temperature steam is delivered to a turbine. Steam generated in this process is expanded in a steam turbine, which drives an electric generator to produce electric power. Steam is later cooled down in a condenser and is pumped back to the boiler to be reheated, completing the cycle.

15 Carnot example

16 Other Carnot Examples