Lesson Plan

Define pressure as P = F/A and use the ideal gas law PV = NkT to relate pressure, volume, and temperature qualitatively (three proportionalities)

Describe pressure–volume work and derive W = PΔV

State the first law of thermodynamics, ΔU = Q − W, both verbally and mathematically, and apply its sign conventions for Q and W

Solve problems using the first law, and explain why internal energy is a state function (path-independent)

12.2

"The ideal gas law states that $PV = NkT$. where P is the pressure of a gas, V is the volume it occupies, N is the number of particles (atoms or molecules) in the gas, and T is its absolute temperature. The constant k is called the Boltzmann constant and has the value $k = 1.38 \times 10^{-23}\text{ J/K}$." "For the purposes of this chapter, we will not go into calculations using the ideal gas law." "Because area multiplied by displacement is the change in volume, $W = P\Delta V$, the mathematical expression for pressure–volume work is $W = P\Delta V$." "Internal energy is the sum of the kinetic and potential energies of a system's atoms and molecules. It can be divided into many subcategories, such as thermal and chemical energy, and depends only on the state of a system (that is, P, V, and T), not on how the energy enters or leaves the system." "The first law of thermodynamics states that the change in internal energy of a closed system equals the net heat transfer into the system minus the net work done by the system. In equation form, the first law of thermodynamics is $\Delta U = Q - W$." "By convention, if Q is positive, then there is a net heat transfer into the system; if W is positive, then there is net work done by the system. So positive Q adds energy to the system by heat, and positive W takes energy from the system by work."