Thermodynamics

Thermodynamics “Movement of Heat” The study of heat and its transformation to mechanical energy. Applications –R–R–R–Refrigerators –H–H–H–Heat pumps –I–I–I–Insulation –H–H–H–Heat engines –E–E–E–Electric generators –F–F–F–Fireplace

Internal Energy (U) Real gas – total kinetic energy of the molecules of the gas and the potential energy due to intermolecular forces. Real gas – total kinetic energy of the molecules of the gas and the potential energy due to intermolecular forces. Ideal gas – total kinetic energy of the molecules (assumes no intermolecular forces) Ideal gas – total kinetic energy of the molecules (assumes no intermolecular forces) –As shown earlier –Internal energy (U) is where N is the number of molecules –So the change in internal energy due to a change in temperature is

Zeroth Law If object A is in thermal equilibrium with object B, and object B is separately in thermal equilibrium with object C, then objects A and C will be in thermal equilibrium if they are placed in thermal contact. Math Speak: Transitive Property Math Speak: Transitive Property If A=B and B=C, then A=C

First Law of Thermodynamics System – set of objects being considered. Whenever heat is added to a system, it transforms to an equal amount of some other form of energy. Whenever heat is added to a system, it transforms to an equal amount of some other form of energy. Heat added to a system can: Heat added to a system can: –Increase the internal energy (temperature) of the system if it remains in the system. –Do external work and leave the system. Opposite is true, work done on a system can increase internal energy. Opposite is true, work done on a system can increase internal energy.

First Law of Thermodynamics Statement of Conservation of Energy If a system’s volume is constant, and heat is added, its internal energy increases

First Law of Thermodynamics If a system does work on its surroundings, and no heat is added, its internal energy decreases.

First Law of Thermodynamics The 1 st Law of Thermodynamics combines these: The change in a system’s internal energy U is related to the heat Q and the work W Sign Conventions:

Thermal Processes Assumptions: Quasi-static – slow enough that the system is always in equilibrium. Reversible – Able to return system and its surroundings to the exact initial conditions. Idealized reversible process: (a) the gas is compressed; the temperature is constant, so heat leaves the gas. (b) the gas expands, it draws heat from the reservoir, returning the gas and the reservoir to their initial states. The piston is assumed frictionless.

P-V Diagrams Graph showing changes in the pressure and volume of a sample of gas Graph showing changes in the pressure and volume of a sample of gas Total work done by the gas is the area under the P-V diagram. Total work done by the gas is the area under the P-V diagram.

Isobaric Process Isobaric - constant pressure Change of V (and T) at constant pressure Work done by an expanding gas

Isobaric Expansion Problem One gram of water is placed in the cylinder and the pressure is maintained at 2.0 x 10 5 Pa. The temperature of the water is raised by 31 C ◦. The water is in the liquid phase and expands by 1.0 x m 3. Find (a) the work done and (b) the change in the internal energy. One gram of water is placed in the cylinder and the pressure is maintained at 2.0 x 10 5 Pa. The temperature of the water is raised by 31 C ◦. The water is in the liquid phase and expands by 1.0 x m 3. Find (a) the work done and (b) the change in the internal energy.

Isochoric Process Isochoric – constant volume (isovolumetric) Change of P (and T) at constant volume Change of P (and T) at constant volume With constant volume there is no movement so no work is done. With constant volume there is no movement so no work is done.

Isothermal Process Isothermal – constant temperature Change in P and V at constant temperature Change in P and V at constant temperature P Pressure varies inversely with the volume.

Isothermal Process The work done is the area under the curve

Isothermal Expansion Problem Two moles of the monatomic gas argon expand isothermally at 298 K, from an initial volume of V 1 =.025 m 3 to a final volume of V f = m 3. Assuming that argon is an ideal gas find (a) the work done by the gas, (b) the change in the internal energy of the gas and (c) the heat supplied to the gas. Two moles of the monatomic gas argon expand isothermally at 298 K, from an initial volume of V 1 =.025 m 3 to a final volume of V f = m 3. Assuming that argon is an ideal gas find (a) the work done by the gas, (b) the change in the internal energy of the gas and (c) the heat supplied to the gas.

Adiabatic Process Adiabatic Adiabatic - no heat flows in or out of the system Change in P and V in an insulated Change in P and V in an insulated container (no heating of the gas) Work is the area under the curve. Work is the area under the curve.

Adiabatic Process PV Curve for an adiabatic process PV Curve for an adiabatic process Isothermal or adiabatic? If an isothermal and an adiabatic have a point in common, then the adiabatic is the curve having the greater slope at that point.

Process Summary Identify the Process: 1.Isochoric 2.Isobaric 3.Isothermal 4.Adiabatic

Idealized vs. Approximate Processes In practice: Isobaric change, trap a small quantity of the gas in a tube using a thread of mercury (or other liquid) and heat it slowly Isobaric change, trap a small quantity of the gas in a tube using a thread of mercury (or other liquid) and heat it slowly Isovolumetric change, heat the gas in a fixed volume container (one made of a material having a low thermal expansivity) Isovolumetric change, heat the gas in a fixed volume container (one made of a material having a low thermal expansivity) Isothermal change, compress (or expand) Isothermal change, compress (or expand) the gas slowly in a container of high thermal conductivity Adiabatic change, compress (or expand) Adiabatic change, compress (or expand) the gas rapidly in a container of low thermal conductivity.

2 nd Law of Thermodynamics Thermal energy always flows spontaneously from a hot object to a cold object. Thermal energy always flows spontaneously from a hot object to a cold object. Thermal energy spontaneously flowing from a cold to hot object is not prevented by the conservation of energy. Why does it not occur? Thermal energy spontaneously flowing from a cold to hot object is not prevented by the conservation of energy. Why does it not occur? 2 nd Law of Thermodynamics

Heat Engine Heat engine - a machine which converts internal energy (from a high temperature body) into some other form of energy. All heat engines have: a high-temperature reservoir (Heat Source) a low-temperature reservoir (Heat Sink) a cyclical engine

2 nd Law of Thermodynamics The conversion of energy from some other form of energy to internal energy of a substance can be done with 100% efficiency of conversion. – –For example, 100J of electrical energy will be converted to 100J of internal energy by a resistor. Conversion of energy from internal energy to some other form cannot be done with the same efficiency.

2 nd Law of Thermodynamics Gas expanding, doing work, pushing piston down. Gas expanding, doing work, pushing piston down. To obtain more work, we must now push the piston back up – –push the piston back up we will do just as much work as produced by the expansion stage – –To do less work allow the gas to cool down before pushing the piston up. Or let this hot gas escape, push the piston up and replace the gas. Regardless, the gas will always give up some of its internal energy to the surroundings (cools down). Therefore, the conversion of energy from internal energy of the hot gas can never be 100% efficient. No heat engine, operating in a continuous cycle, can do work without transferring some internal energy from a hot body to a cold body.

Heat Engine During each cycle: W is the net work done by the engine W is the net work done by the engine Q H is the energy taken from the (hot) source Q H is the energy taken from the (hot) source Q C is the energy given to the (cold) sink Q C is the energy given to the (cold) sink Efficiency ( or ) : Efficiency (e or η) :

Carnot’s Principle The maximum efficiency of an engine operating between two constant- temperature reservoirs occurs only when all processes are reversible. Reversible process – both system and its environment can be returned to the exact conditions prior to when the process began. All reversible engines operating between the same two temperatures, T c and T h, have the same efficiency. Idealization; no real engine can be perfectly reversible.

Carnot’s Principle Carnot’s principle implies that the efficiency depends only on the two temperatures. Therefore, So, the maximum efficiency of a heat engine:

Carnot’s Principle The efficiency is zero when the two reservoirs are at the same temperature. The smaller the ratio of T c to T h, the closer the efficiency will be to 1. Maximum Work of a Heat Engine

Carnot’s Engine 1. Gas at temperature T H 2. Gas at temperature T H placed in contact with heat source at temperature T H. 3. Isothermal expansion at T H (slow expansion). Work done by the gas. 4. Gas removed from source and insulated.

Carnot’s Engine 5. Adiabatic expansion until temperature reaches T C. Work done by the gas. 6. Gas at temperature T C placed in contact with heat sink at temperature T C. 7. Isothermal compression at T C (slow compression). Work done on the gas. 8. Adiabatic compression until temperature reaches T H.

PV diagram – Carnot Engine Curve A (2 to 3) Isothermal expansion at T H Work done by the gas Curve B (4 to 5) Adiabatic expansion. Work done by the gas Curve C (6 to 7) Isothermal compression at T C Work done on the gas Curve D (8 to 1) Adiabatic compression Work done on the gas

PV diagram – Carnot Engine Since, the product of pressure and volume represents a work This is represented by the area below a p-V curve. The area enclosed by the four curves represents the net work done by the engine during one cycle.

Carnot’s Engine Theoretical engine designed for maximum efficiency. Theoretical engine designed for maximum efficiency.Assumptions All processes are reversible All processes are reversible No friction is present and the internal energy transfers take place under conditions very close to thermal equilibrium. No friction is present and the internal energy transfers take place under conditions very close to thermal equilibrium. Expansions occur at high temperatures, compressions occur at lower temperatures. Expansions occur at high temperatures, compressions occur at lower temperatures. Work done by the gas is greater than work done on the gas Work done by the gas is greater than work done on the gas Cycle’s net effect is W= Q H -Q C has been done and thermal energy Q C has been transferred from the source to the sink. Cycle’s net effect is W= Q H -Q C has been done and thermal energy Q C has been transferred from the source to the sink. Process reversed results in an external agent doing work, W, transferring internal energy, Q, from the sink to the source. Process reversed results in an external agent doing work, W, transferring internal energy, Q, from the sink to the source.

Heat Pump Review - Heat will flow spontaneously only from a higher temperature to a lower one. However, If work is done to the system, heat can be made to flow from a lower temperature to a higher temperature. If a heat engine is operated in reverse it transfers internal energy from a body at a low temperature to one at a higher temperature. Refrigerators, air conditioners, and heat pumps

Heat Pump Since work is used to extract heat from the cold reservoir to the hot reservoir. Since work is used to extract heat from the cold reservoir to the hot reservoir. An ideal refrigerator would remove the most heat from the interior while requiring the smallest amount of work. This ratio is called the coefficient of performance, COP: Typically, COP values between 2 and 6. Bigger is better!

Ideal Heat Pump In an ideal heat pump with two operating temperatures (cold and hot), the Carnot relationship holds; the work needed to add heat Q h to a room is: The COP for this ideal heat pump:

Refrigerator 1. Compressor compresses refrigerant gas. Gas condenses to a liquid. Condensation is exothermic, heat released. This is why coils feel warm. 2. Liquid refrigerant flows through the expansion valve toward the inside of the refrigerator.

How a Refrigerator Works 3. When fluid passes through expansion valve, the liquid moves from a high pressure zone to a low pressure zone, so it evaporates. Evaporation is endothermic and absorbs heat, making the inside of the refrigerator cold. 4. The gas returns to the coils outside the fridge where it is compressed and condensed. Heat is released.

Cool Question If your air conditioning breaks, can you open the door to the refrigerator and use it to cool your house? If your air conditioning breaks, can you open the door to the refrigerator and use it to cool your house?

Cool Question - defrosted The phase change, liquid to vapor (inside the fridge), occurs at low temperature. During this phase change, latent heat of vaporization is taken in. The phase change, liquid to vapor (inside the fridge), occurs at low temperature. During this phase change, latent heat of vaporization is taken in. When the vapor is compressed there is an increase in temperature. The phase change, vapor to liquid (outside the fridge), occurs at high temperature. Latent heat of vaporization is given out but also heat will be lost as the liquid cools down to the same temperature as the surroundings. When the vapor is compressed there is an increase in temperature. The phase change, vapor to liquid (outside the fridge), occurs at high temperature. Latent heat of vaporization is given out but also heat will be lost as the liquid cools down to the same temperature as the surroundings. Heat taken in Q in = mL v Heat taken in Q in = mL v Heat given out Q out = mL v + mcΔT Heat given out Q out = mL v + mcΔT Obviously, the heat given out is greater Obviously, the heat given out is greater than the heat taken in. So your mom was right, keep the So your mom was right, keep the refrigerator door shut!

Another Cool Question How is an air conditioner configured differently so that it can be used to cool your house? How is an air conditioner configured differently so that it can be used to cool your house?

Air Conditioner The cold reservoir is the interior of the house or other space being cooled, and the hot reservoir is outdoors. Exhausting an air conditioner within the house will result in the house becoming warmer

Heat Pump Heat is removed from the cold reservoir outside, and exhausted into the house, keeping it warm. Work the pump does contributes to warming the house.

Heat Pump

Entropy A reversible engine has the following relation between the heat transferred and the reservoir temperatures: Rewriting, This quantity, Q/T, is the same for both reservoirs, and is defined as the change in entropy. Clausius named it the change in entropy, ΔS

Entropy A real engine will operate at a lower efficiency than a reversible engine; meaning less heat is converted to work. Valid only for heat transfer which is reversible In a reversible heat engine, it can be shown that the entropy does not change. Any irreversible process results in an increase of entropy.

Entropy & Disorder At absolute zero (0K) the atoms of a substance are stationary. They form a well ordered arrangement. When energy flows into a body its atoms vibrate, they become a less well ordered arrangement At absolute zero (0K) the atoms of a substance are stationary. They form a well ordered arrangement. When energy flows into a body its atoms vibrate, they become a less well ordered arrangement  energy entering a body increases disorder  energy leaving a body decreases disorder Boltzmann showed that changes in entropy of a body is a direct measure of changes in the disorder of the arrangement of the particles.

Entropy Assumption: quantity of energy, ΔQ, which flows from the hot to the cold body is so small that it does not significantly change the temperatures T 1 and T 2. Each body will experience a change in the entropy of its particles. Each body will experience a change in the entropy of its particles. The hot body experiences a decrease in entropy (a negative change) of magnitude ΔS 1 = ΔQ/T 1 The hot body experiences a decrease in entropy (a negative change) of magnitude ΔS 1 = ΔQ/T 1 The cold body experiences an increase in entropy (a positive change) of magnitude ΔS 2 = ΔQ/T 2 The cold body experiences an increase in entropy (a positive change) of magnitude ΔS 2 = ΔQ/T 2 The net change in entropy ΔS = ΔS 1 + ΔS 2. The net change in entropy ΔS = ΔS 1 + ΔS 2. Now T 2 < T 1 so ΔQ/T 2 must be greater than ΔQ/T 1. Now T 2 < T 1 so ΔQ/T 2 must be greater than ΔQ/T 1. Therefore, the net change in entropy due to this naturally occurring process must be greater than zero. Therefore, the net change in entropy due to this naturally occurring process must be greater than zero. This leads to the following alternative statement of the second law of thermodynamics. This leads to the following alternative statement of the second law of thermodynamics.

Entropy – 2 nd Law of Thermodynamics The total entropy of the universe increases whenever an irreversible process occurs. The total entropy of the universe is unchanged whenever a reversible process occurs. Since all natural occurring processes are irreversible: The effect of naturally occurring processes is always to increase the total entropy (or disorder) of the universe. As the total entropy of the universe increases, its ability to do work decreases. The excess heat exhausted during an irreversible process cannot be recovered; doing that would require a decrease in entropy.

Third Law of Thermodynamics It is impossible to lower the temperature of an object to absolute zero in a finite number of steps. Absolute zero is a temperature that an object can get arbitrarily close to, but never attain. Temperatures as low as 2.0 x K have been achieved in the laboratory, but absolute zero will remain ever elusive – there is simply nowhere to “put” that last little bit of energy.

PPT Sources James S. Walker Physics, 3rd Edition © 2007 Pearson Prentice Hall Cutnell & Johnson, Physics 5 th Edition Wiley Publishing The Open Door Website Tsokos, K.A. Physics for the IB Diploma, 4 th Edition Cambridge University Press