## Lecture 18: First Law of Thermodynamics and Gas Processes

October 31, 2017

### Objectives

• (Continuing objective) Be able to relate concepts of thermodynamics and statistical mechanics to “everyday” situations and to discuss various applications of the concepts to practical problems in various fields of science, medicine and engineering.
• Draw and/or interpret a P-V diagram for a thermodynamic process or a series of processes occurring in a fixed quantity of ideal gas.
• Calculate the work done by the gas during a thermodynamic process, either from the area under the curve on a P-V diagram or by integration.
• Describe the following ideal gas processes and what quantity is constant (in terms of P, V, and T) for each process: (a) constant volume process, (b) constant pressure process, (c) isothermal process, (d) adiabatic process.
• For a series of ideal gas processes, calculate the pressure, volume and temperature for each state and the change in internal energy, heat added, work done on and work done by for each process, using the ideal gas law or the first law of thermodynamics when needed.

### Homework

• Wednesday's Assigned Problems: Supp CH 8: 1, 2, 3, 4, 7, 8, 9, 11, 13, 15

#1 most: adiabatic, least: isobaric; #3 (a) fast compression (it's also possible to have adiabatic if encased in insulation, but that isn't what happens in a car engine), (b) from work done on the gas by the piston; #7 $-46\,\text{J}$; #8 0 J; #9 (a) 0.21 moles, (b) +877 J, (c) -877 J; #11 (a) $\Delta E_\text{therm} = nR\Delta T$, (b) $\frac{3}{2}nR\Delta T$; #13 379 kPa; #15 $A \to B$: $Q_\text{in} = 0$, $W_\text{on} = 116 \,\text{J}$, $B \to C$: $\Delta E_\text{therm} = 371$ J, $Q_\text{in} = 520$ J, $W_\text{on} = -149$ J; $C \to A$: $\Delta E_\text{therm}$ = -488 J, $W_\text{on} = 0$ J, $Q_\text{in} = -488$ J, Entire cycle: $\Delta E_\text{therm} = -1$ J (Actually, this should be zero, but there are accumulated rounding errors here), $W_\text{on} = -33$ J, $Q_\text{in} = 32$ J

• Monday's Hand-In Problems: Supp CH 8: 5, 6, 12, 14, 16; Supp CH 9: 10, 11, 12, 13, 15, 17

### Videos of example problems

To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.
• Video Example #1. This video example is a very long example of a cyclic process with nearly all of the special case thermodynamic processes in it. It demonstrates how to draw a P-V diagram and lots of use of the ideal gas law. There are many calculations using the First Law of Thermodynamics, the definition of the thermal energy of a monatomic gas, along with determining the work done by the gas. It also gives an example of how to use the adiabatic relation pVγ = constant. Note that the thermal energy ΔEtherm is called the internal energy and written as ΔU in these examples.

• Video Example #2: Using the First Law of Thermodynamics. Note that ΔU is the same as ΔEtherm, and W in this example refers to the work done by the gas during the process, rather than the work done on the gas. (Recall: Won = -Wby.). ans: 85 J is added to the system

### Drinking bird tweet of the day

(Note that we have a new, larger momma bird -- the latest additions to our drinking bird collection.)

### Pre-Class Entertainment

• Once Upon a Time in the West, by Dire Straits
• On Melancholy Hill, by the Gorillaz
• Orinoco Flow, by Enya
• Orange Crush, by REM