Thermodynamics is all about energy.

Internal energy is a measure of the total kinetic energy of the atoms and molecules. It is directly proportional to temperature.

First Law: ΔE_int = Q - W

Ideal gas law: PV = nRT or PV = NkT

Work is the area under the P-V curve. It depends on the process.

The change in internal energy ΔE_int is independent of the process, depending only on the change in temperature.

C_V depends on whether the gas is monatomic, diatomic, etc.

The heat also depends on the process.

Process	Basic Idea	Work (W)	ΔEint	Heat (Q)
Isochoric (Constant Volume)	W = 0	0	n CV ΔT	Q = ΔEint
Isothermal (Constant Temp.)	ΔEint = 0	nRT ln ( Vf Vi )	0	Q = W
Adiabatic (No Heat)	Q = 0	PVγ = constant Integrate to get W	ΔEint = -W	0
Free Expansion	Q = 0; ΔT = 0	0	0	0
Isobaric (Constant Pressure)	no zeroes!	PΔV = nR ΔT	n CV ΔT	n CP ΔT