First Law of Thermodynamics: Thermal Energy and Work

"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."