Thermodynamics systems • A thermodynamic system is any collection of objects that may exchange energy with its surroundings. • The popcorn in the pot is a thermodynamic system. • In the thermodynamic process shown here, heat is added to the system, and the system does work on its surroundings to lift the lid of the pot.
© 2016 Pearson Education Inc. Thermodynamics systems • In a thermodynamic process, changes occur in the state of the system. • Careful of signs! • Q is positive when heat flows into a system. • W is the work done by the system, so it is positive for expansion.
© 2016 Pearson Education Inc. Ideal-Gas Processes
. An ideal-gas process can be represented on a graph of pressure versus volume, called a pV diagram. . Knowing p and V, and assuming that n is known for a sealed container, we can find the temperature T by using the ideal-gas law. . Here is a pV diagram showing three states of a There are infinitely many system consisting of 1 mol ways to change the gas of gas. from state 1 to state 3.
© 2017 Pearson Education, Inc. Slide 18-3 Ideal-Gas Processes
. (a) If you slowly pull a piston out, you can reverse the process by slowly pushing the piston in. . This is called a quasi-static process. . (b) is a sudden process, which cannot be represented on a pV diagram. . Quasi-static processes keep the system in thermal equilibrium.
© 2017 Pearson Education, Inc. Slide 18-4 Work done during volume changes • We can understand the work done by a gas in a volume change by considering a molecule in the gas. • When one such molecule collides with a surface moving to the right, so the volume of the gas increases, the molecule does positive work on the piston.
© 2016 Pearson Education Inc. Work done during volume changes • If the piston moves toward the left as in the figure shown here, so the volume of the gas decreases; positive work is done on the molecule during the collision. • Hence the gas molecules do negative work on the piston.
© 2016 Pearson Education Inc. Work done during volume changes • The infinitesimal work done by the system during the small expansion dx is dW = pA dx.
• In a finite change of
volume from V1 to V2:
© 2016 Pearson Education Inc. Work on a pV-diagram • The work done equals the area under the curve on a pV-diagram. • Shown in the graph is a system undergoing an expansion with varying pressure.
© 2016 Pearson Education Inc. Work on a pV-diagram • Shown in the graph is a system undergoing a compression with varying pressure. • In this case the work is negative.
© 2016 Pearson Education Inc. Work on a pV-diagram • Shown in the graph is a system undergoing an expansion with constant pressure.
• In this case, W = p(V2 – V1)
© 2016 Pearson Education Inc. Example 1 – As an ideal gas undergoes an isothermal (constant-temperature) expansion at temperature T, its volume changes from V1 to V2. How much work does the gas do? Work depends on the path chosen: Slide 1 of 4 • Consider three different paths on a pV-diagram for getting from state 1 to state 2.
© 2016 Pearson Education Inc. Work depends on the path chosen: Slide 2 of 4 • The system does a large amount of work under the path
© 2016 Pearson Education Inc. Work depends on the path chosen: Slide 3 of 4 • The system does a small amount of work under the path
© 2016 Pearson Education Inc. Work depends on the path chosen: Slide 4 of 4 • Along the smooth curve from 1 to 2, the work done is different from that for either of the other paths.
© 2016 Pearson Education Inc. QuickCheck
This p-V diagram shows two ways to take a system from state a (at lower left) to state c (at upper right): • via state b (at upper left), or • via state d (at lower right) For which path is W > 0? A. path abc only B. path adc only C. both path abc and path adc D. neither path abc nor path adc First law of thermodynamics • The change in the internal energy U of a system is equal to the heat added minus the work done by the system:
• The first law of thermodynamics is just a generalization of the conservation of energy. • Both Q and W depend on the path chosen between states, but is independent of the path. • If the changes are infinitesimal, we write the first law as dU = dQ – dW.
© 2016 Pearson Education Inc. First law of thermodynamics • In a thermodynamic process, the internal energy U of a system may increase. • In the system shown below, more heat is added to the system than the system does work. • So the internal energy of the system increases.
© 2016 Pearson Education Inc. First law of thermodynamics • In a thermodynamic process, the internal energy U of a system may decrease. • In the system shown below, more heat flows out of the system than work is done. • So the internal energy of the system decreases.
© 2016 Pearson Education Inc. First law of thermodynamics • In a thermodynamic process, the internal energy U of a system may remain the same. • In the system shown below, the heat added to the system equals the work done by the system. • So the internal energy of the system is unchanged.
© 2016 Pearson Education Inc. QuickCheck You put a flame under a piece of metal, raising the temperature of the metal and making the metal expand. The metal is surrounded by air. What are the signs of ∆U, Q, and W for the metal in this process?
A. ∆U > 0, Q > 0, W > 0 B. ∆U < 0, Q > 0, W > 0 C. ∆U > 0, Q > 0, W < 0 D. ∆U < 0, Q > 0, W < 0
© 2016 Pearson Education, Inc. The First Law of Thermodynamics
. An isothermal process is one for which the temperature of a specific amount of gas is held constant (no change in total thermal energy). . An isochoric process is one for which the volume of the gas is held constant. . An adiabatic process is one in which no heat energy is transferred.
∆퐸푡ℎ= 푄 − 푊
© 2017 Pearson Education, Inc. Slide 18-22 QuickCheck A cylinder of gas has a frictionless but tightly sealed piston of mass M. Small masses are placed onto the top of the piston, causing it to slowly move downward. A water bath keeps the temperature constant. In this process:
A. Q > 0 B. Q = 0 C. Q < 0 D. There’s not enough information to say anything about the heat.
© 2017 Pearson Education, Inc. Slide 18-23 QuickCheck A system can be taken from state a to state b along any of the three paths shown in the p-V diagram. If state b has greater internal energy than state a, along which path is the absolute value |Q| of the heat transfer the greatest?
A. path 1 B. path 2 C. path 3 D. |Q| is the same for all three paths.
© 2016 Pearson Education, Inc. QuickCheck A system can be taken from state a to state b along any of the three paths shown in the p-V diagram. If state b has greater internal energy than state a, along which path is there a net flow of heat out of the system?
A. path 1 B. path 3 C. all of paths 1, 2, and 3 D. none of paths 1, 2, or 3
© 2016 Pearson Education, Inc. Example 2 – You propose to climb several flights of stairs to work off the energy you took in by eating a 900-calorie hot fudge sundae. How high must you climb? Assume your mass is 80.0 kg and a 25% efficiency of converting food energy to mechanical energy. Example 3 – One gram of water (1 cm3) becomes 1671 cm3 of steam when boiled at a constant pressure of 1 atm. Compute the work done by the water when it vaporizes and its increase in internal energy
Note: The increase in internal energy is used to dissociate the water molecules as it turns to steam. It will not increase the temperature of the steam. Example 4 – The figure below shows a pV-diagram for a cyclic process in which the initial and final states of some thermodynamic system are the same. The state of the system starts at point a and proceeds counterclockwise in the diagram to point b, then back to a; the total work is W = -500J. Why is the work negative? Also, Find the change in internal energy and the heat added during this process. In-class Activity #1 – The pV-diagram below shows a series of thermodynamic processes. In process ab, 150 J of heat is added to the system; in process bd, 600 J heat is added. Find (a) the internal energy change in process ab; (b) the internal energy change in process abd; and (c) the total heat added in process acd. Special Ideal-Gas Processes
. There are three ideal-gas processes in which one of the three terms in the
first law—∆Eth, W, or Q—is zero:
• Isothermal process (∆ Eth = 0): If the temperature of a gas doesn’t change, neither does its thermal energy. So, the first law is W = Q. • Isochoric process (W = 0): Work is done on (or by) a gas when its volume changes. An isochoric process has ∆V = 0; thus no work is done
and the first law can be written ∆Eth = Q. • Adiabatic process (Q = 0): A process in which no heat is transferred— perhaps the system is extremely well insulated—is called an adiabatic process. The system is thermally isolated from its environment.
With Q = 0,the first law is ∆Eth = – W.
Isobaric process: The pressure remains constant, so W = p(V2 – V1).
© 2017 Pearson Education, Inc. Slide 18-30 The four processes on a pV-diagram • Shown are the paths on a pV-diagram for all four different processes for a constant amount of an ideal gas, all starting at state a.
© 2016 Pearson Education Inc. QuickCheck
What type of gas process is this?
A. Isochoric B. Isobaric C. Isothermal D. Adiabatic E. None of the above
© 2017 Pearson Education, Inc. Slide 18-32 QuickCheck An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. For process a b,
A. Q > 0, ∆U > 0 B. Q > 0, ∆U = 0 C. Q = 0, ∆U > 0 D. Q = 0, ∆U < 0
© 2016 Pearson Education, Inc. QuickCheck An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. For process b c,
A. Q > 0, ∆U > 0 B. Q > 0, ∆U = 0 C. Q = 0, ∆U > 0 D. Q = 0, ∆U < 0
© 2016 Pearson Education, Inc. QuickCheck An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. For process c a,
A. Q > 0, ∆U > 0 B. Q = 0, ∆U > 0 C. Q = 0, ∆U < 0 D. Q < 0, ∆U < 0
© 2016 Pearson Education, Inc. QuickCheck
An ideal gas is taken around the cycle shown in this p-V diagram, from a to b to c and back to a. Process b c is isothermal. For this complete cycle,
A. Q > 0, W > 0, U = 0 B. Q < 0, W > 0, U = 0 C. Q = 0, W > 0, U < 0 D. Q = 0, W < 0, U > 0
© 2016 Pearson Education, Inc.